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המכניס ידיו לבית המנוגע ידיו תחילות (a person who pokes his hands into a leprous house -his hands are first degree of uncleanness) – it invalidates first degree in non-sacred matters, for something that is first-degree of uncleanness makes something second-degree of uncleanness in non-sacred things. And defiles first degree and invalidates first degree of uncleanness with heave-offering/Terumah. And it defiles two things and invalidates one in holy things.

If a person puts his hands inside a house with scale disease, his hands have first degree uncleanness, the words of Rabbi Akiba. But the sages say: his hands have second degree uncleanness.
Whoever defiles garments: at the time when he touches [the uncleanness], he defiles hands so that they have first degree uncleanness, the words of Rabbi Akiba. But the sages say: such that they have second degree of uncleanness.
They said to Rabbi Akiba: where do we find anywhere that hands have first degree uncleanness? He said to them: but how is it possible for them to become unclean with first degree uncleanness without his whole body becoming unclean? Only in these cases [can they have first degree uncleanness].
Foods and vessels which have been defiled by liquids convey second degree of uncleanness to the hands, the words of Rabbi Joshua. But the sages say: that which has been defiled by a father of uncleanness conveys uncleanness to the hands, but that which has been defiled by an offspring of uncleanness does not defiled the hands.
Rabban Shimon ben Gamaliel said: it happened that a certain woman came before my father and said to him, "My hands went into the air-space inside an earthenware vessel." He said to her: "My daughter, what was the cause of its uncleanness?" But I did not hear what she said to him. The sages said: the matter is clear that which has been defiled by a father of uncleanness conveys uncleanness to the hands, but that which has been rendered unclean by an offspring of uncleanness does not defiled the hands.
Section one: In Tractate Negaim we learned about the house that has some sort of scale disease. Rabbi Akiva says that if someone puts just his hands into such a house, the hands have first degree uncleanness. The other sages say that his hands only have second degree uncleanness.
Second two: There is a similar dispute concerning a person who defiles garments. This is a about whom the Torah says that he must wash his clothes: for instance one who touches a zav or one who touches something a zav lied upon, or who touches a zavah or a menstruant. According to Rabbi Akiva when such a person is touching the source of uncleanness, another person who touches him will get first degree uncleanness in his hands. The other sages say that he will get second degree uncleanness.
Section three: The other sages now argue with Rabbi Akiva, asking him where we find that hands can have first degree impurity.
Rabbi Akiva responds that in essence they are right. Hands can only have first degree impurity if the whole body also has first degree impurity. However, these cases in sections one and two are exceptions for in these cases the body wasn't defiled at all. Only in these cases can someone's hands have first degree impurity while the rest of his body remains pure.
Section four: We find a similar dispute regarding foods and vessels which have been defiled by liquids. These foods now have second degree impurity (see Zavim 5:12). According to Rabbi Joshua they defile hands such that the hands have second degree impurity. The other rabbis say that only foods or vessels that were defiled by a father of uncleanness and thereby have first degree impurity can defile hands. But if foods have only second degree impurity, they don't defile hands at all.
Section five: Rabban Shimon ben Gamaliel now cites a story about a woman who came in front of Rabban Gamaliel, his father. The woman's hands had gone into the air-space of an impure earthenware vessel. Such vessels convey impurity through their air-space. Rabban Gamaliel asks her if the vessel had received its impurity from contact with a father of uncleanness or whether the vessel was defiled by something with first degree uncleanness? Unfortunately, Rabban Shimon ben Gamaliel never heard the response (those kids, they're never listening!).
The sages say that their halakhah from section four is applicable here. If the earthenware vessel had received impurity from a father of uncleanness then her hands would have second degree uncleanness. But if the vessel had been defiled by something with first degree uncleanness, her hands would be pure.

כל המטמא בגדים בשעת מגעו – as for example the flux of a person with gonorrhea and his spittle, and all of these are taught in the last chapter [Five] of [Tractate] Zavim [Mishnah 7] that a person who comes in contact with them defiles clothing at the time of his contact (see Mishnah 1 of that chapter).

וכי היאך אשפר להן להיות תחילה – for it is not worthy to become first degree of uncleanness other than if that person came in contact with a primary source of ritual uncleanness. But if his hands came in contact with a primary source of ritual uncleanness, all of his body is defiled. Therefore, it is not in my hands to find the hands as a first-degree of ritual uncleanness, other than one pokes his hands into a leprous house, for if he poked his hands, he was not defied entirely, but if he defiles his clothing at the time of his contact, even though he is considered a primary source of ritual uncleanness to defile clothing and make something first-degree and second-degree of ritual uncleanness, he is not considered a primary source of uncleanness to defile a person, but he defiles the hands that came in contact with it to be first-degree of ritual uncleanness. But the Halakha is not according to Rabbi Akiva.

את שנטמא באב הטומאה – that is to say, food and utensils/vessels that were defiled by a primary source of ritual uncleanness.

מטמאין את הידים – but not food nor utensils/vessels that were defiled by liquids, for something that is second-degree ritual uncleanness does not make something second-degree ritual uncleanness. And the Halakha is according to the Sages.

במה היתה הטומאה – of the oven, through a primary source of ritual uncleanness or through a liquid.

כל הפוסל את התרומה – that is second degree ritual impurity (i.e., food that became ritually impure through contact with first degree ritual impurity. It renders Terumah/heave-offering with third degree ritual impurity. The Sages decreed that sacred books/scrolls and unwashed hands have second degree ritual impurity status).

Introduction This mishnah continues with a dispute between Rabbi Joshua and the sages. As part of their argument they mention the concept that the Holy Scriptures, meaning the Tanakh or Bible, defile the hands. This is a topic that will be discussed throughout the remainder of the chapter. There are two explanations for this halakhah. The traditional explanation is a bit strange and convoluted but it goes like this. People used to store their terumah near the same place that they stored holy scrolls (the Tanakh). Mice would come to eat the terumah and would also eat through the scrolls. To prevent this, the rabbis declared that the scrolls would defile the terumah. This would discourage people from storing terumah near their scrolls. One can clearly sense that this simply does not seem likely to have been the origins of this idea. Recently, academic scholars have explained that according to some laws in the Torah holiness can "rub off" on an item with which it has contact. This rubbing off on the item works a little bit like impurity, except the terminology is not that the item becomes "impure" rather it becomes "holy." The rabbis inherited the concept that scrolls of Scripture were so holy that anything they touched would become "holy" as well. Since this was the only such situation that the rabbis encountered, they used the normal term for such "rubbing off" which is impurity. In other words, what really seems to happen is that the hands become holy by virtue of contact with the scrolls. Nevertheless, by the time of the Mishnah these laws are part of the general purity system.

מטמאה את חברתה – Whomever had one hand impure and it came in contact with his other pure hand, it becomes defiled, and both of them returned ritually impure.

Anything which disqualifies terumah defiles hands with a second degree of uncleanness. Anything that has even second degree uncleanness will defile the hands so that they too have second degree uncleanness. This accords with Rabbi Joshua's opinion in yesterday's mishnah. The other rabbis disagree.

והלא כתבי הקודש – that they (i.e., the Rabbis) decreed that they (i.e., sacred books/scrolls) are second degree ritual impurity and they invalidate the heave-offering/Terumah (i.e., priest’s due), and they defile the hands that come in contact with them to be second [degree ritually impure], so we see that something second degree ritually impure makes [something else] second [degree ritually impure].

One [unwashed] hand defiles the other hand, the words of Rabbi Joshua. But the sages say: that which has second degree of uncleanness cannot convey second degree of uncleanness. An unwashed hand has second degree uncleanness and therefore it disqualifies terumah. According to Rabbi Joshua this means that if one hand is unwashed and it touches a washed hand it will defile it. The sages reject his opinion, as they did in yesterday's mishnah, holding that something that has second degree impurity cannot convey impurity to anything else. All it can do is disqualify terumah.

ולא דברי סופרים מדברי סופרים – but the defilement of the hands of all of the defilements, is from the words of the Scribes (i.e., Rabbinic law – generally from the period of Ezra), for Shlomo (i.e., King Solomon) established [the laws of] Eruvin/Sabbath limits and hands [which are not found in the Written Torah]. And Holy Writ that defiles the hands is also from the words of the Scribes, which is from the eighteen matters (i.e., actually decrees) that they made on that day (i.e., when Rabban Gamaliel was deposed: see Talmud Berakhot 28a). But we do not judge/make a ruling from this case to that one to state that just as we found that Holy Scrolls that are second [degree of ritual impurity] make [something else] second [degree of ritual impurity], so here also in the remainder of the defilements that will be that something second [degree ritual impurity] will make [something else] second [degree ritual impurity, for what was established was established was established [and] what was not established was not established. But the Halakha is not according to Rabbi Yehoshua.

He said to them: But do not the Holy Scriptures which have second degree of uncleanness defile the hands? They said to him: the laws of the Torah may not be argued from the laws of the scribes, nor may the laws of the scribes be argued from the laws of the Torah, nor may the laws of the scribes be argued from [other] laws of the scribes. Rabbi Joshua uses the concept of the Holy Scriptures defiling the hands as proof for his opinion that anything with second degree uncleanness conveys uncleanness to hands. According to the rabbis, the Tanakh has second degree uncleanness and it defiles the hands. Therefore, everything that has second degree uncleanness should similarly defile the hands. The other rabbis reject learning from one category of rabbinic law to another. The idea that the Tanakh defiles the hands is a "law of the scribes" it is of rabbinic origin. Similarly, the halakhah that unwashed hands defile terumah is also of rabbinic origin (see the introduction). One cannot use one halakhah of rabbinic origin to prove another halakhah.

רצועות של תפילין מטמאות את הידים – that when they (i.e., the Rabbis) made the decree on [the defiling of] the hands that comes on account of a scroll that invalidates the heaven offering, they decreed also on the hands that came in contact with the straps of the Tefillin/phylacteries.

The straps of the tefillin [when connected] with the tefillin [boxes] defile the hands. Tefillin boxes have scrolls of Scripture in them. Therefore, they clearly would defile the hands. According to the first opinion, the straps do as well, as long as they are tied to the tefillin boxes.

ר' שמעון אומר כו' – But the Halakha is not according to Rabbi Shimon.

Rabbi Shimon says: the straps of the tefillin do not defile the hands. Rabbi Shimon says that the straps do not defile the hands, since they are only connected to the boxes they don't have the scrolls in them.

שמלמעלן ושמלמטן (the upper and lower margins) - that he (i.e., the Scribe) needs to leave free without writing above from the column [in the parchment] three fingerbreadths and one handbreadth below.

The margin on a scroll which is above or below or at the beginning or at the end defiles the hands. Although there is nothing written in the margins of the Tanakh scrolls, they still defile the hands because they are part of the scroll.

שבתחילה ושבסוף – at the beginning of the Scroll he needs to leave free in order to roll all of the Scroll, meaning to say, like the measurement of the circumference of the entire Scroll, that the Scroll, when t is rolled from its end to its beginning is similar to a Mezuzah when they fold it from [the word] אחד/[“God is] one,” directed towards the שמע/[first word of the] Shema. And at its conclusion in order to roll up the scroll of the Law around a cylinder (i.e., a handle). And especially when he doesn’t have anything there other than the Torah alone, he needs to do this, but when he fastens the [text of the] Torah, [the text of] the Prophets and [the text of] the Writings together, he needs to roll up the all of the Scroll at its end, in order to roll the cylinder at its beginning. But if he rolls it towards its beginning, it is found that the Torah (i.e., Five Books of Moses) is from the outside, and it is disgraceful that that Torah should be made into a guardian for the Prophets and the Writings. And it is this that we are speaking f in the first chapter of Bava Batra [13b-14a] and he makes it in order to roll [enough blank parchment wrapped around a cylinder from its beginning and in order that there be a circumference of the Scroll at its end.

Rabbi Judah says: the margin at the end does not render unclean [the hands] until a handle is fastened to it. Rabbi Judah says that the margin at the end of the scroll doesn't defile because it could always be cut off. It only defiles once they have used that extra piece of scroll to attach a handle. Once a handle has been attached the end margin has become a necessary part of the scroll and it too defiles.

כפרשת ויהי בנוסע הארון – because since that portion (Numbers 10:35-36) is considered like a Scroll (i.e., book of the Torah) by itself. And similarly, they stated in the Midrash Yelamdenu [regarding] (Proverbs 9:1): “[Wisdom has built her house,] She has shewn her seven pillars,” these are seven Scrolls of the Torah, since the book [of] “And God spoke” (i.e., referring to the Book of Numbers) was divided into three parts, and [there are] four other books (i.e., Genesis, Exodus, Leviticus and Deuteronomy), hence there are seven [books of the Torah]. (see Talmud Shabbat 116a and especially the first Tosafot that explains this Midrash on how the Israelites left Mount Sinai in a desire to discard their learning.)

A scroll on which the writing has become erased and eighty-five letters remain, as many as are in the section beginning, "And it came to pass when the ark set forward" (Numbers 10:35-36) defiles the hands. A single sheet on which there are written eighty-five letters, as many as are in the section beginning, "And it came to pass when the ark set forward", defiles the hands.
All the Holy Scriptures defile the hands.
The Song of Songs and Kohelet ( defile the hands.
Rabbi Judah says: the Song of Songs defiles the hands, but there is a dispute about Kohelet.
Rabbi Yose says: Kohelet does not defile the hands, but there is a dispute about the Song of Songs.
Rabbi Shimon says: [the ruling about] Kohelet is one of the leniencies of Bet Shammai and one of the stringencies of Bet Hillel.
Rabbi Shimon ben Azzai said: I have received a tradition from the seventy-two elders on the day when they appointed Rabbi Elazar ben Azariah head of the academy that the Song of Songs and Kohelet defile the hands.
Rabbi Akiba said: Far be it! No man in Israel disputed that the Song of Songs [saying] that it does not defile the hands. For the whole world is not as worthy as the day on which the Song of Songs was given to Israel; for all the writings are holy but the Song of Songs is the holy of holies. If they had a dispute, they had a dispute only about Kohelet.
Rabbi Yohanan ben Joshua the son of the father-in-law of Rabbi Akiva said in accordance with the words of Ben Azzai: so they disputed and so they reached a decision.
Today's mishnah contains a fascinating argument over whether two books from the Tanakh, Kohelet (Ecclesiastes) and the Song of Songs (Shir Hashirim) defile the hands. This is basically an argument over whether these books should be included in the Biblical canon. We cannot be certain why there was an argument over these specific books. Probably the content of these books caused certain sages to wish to cut them out of the canon. Kohelet is a deeply skeptical work, one which frequently questions whether the world works justly. One central message of the book is that the righteous and the evil receive the same lot in this world. Sometimes life is even worse for the righteous than it is for the evil. Song of Songs seems to be a love song between a man and a woman. What place does such literature have, some rabbis asked, in the biblical canon? In the end, both books were accepted into the canon and have been found in Jewish (and non-Jewish) bibles ever since.
Section one: The smallest "parsha" in the Torah is Numbers 11:35-36. These two verses, which contain 85 letters, are set off as a "parsha" in the traditional writing of the Torah. The mishnah uses this number as a paradigm for what constitutes a "scroll" such that it would defile the hands. There either have to remain 85 letters from a scroll that used to have more, or a new scroll has to already have 85 letters. Less than 85 letters and the scroll will not defile the hands.
Sections 2-9: The remainder of the mishnah is an extended discussion/argument over whether two books, Kohelet and Shir Hashirim (Ecclesiastes and Song of Songs) defile the hands (i.e. are they part of the canon).
Ultimately, we know that both of these books were accepted into the Jewish Bible, and indeed were rich sources for rabbinic midrashim. There are probably several reasons why they were accepted. First and foremost, Shir Hashirim is explicitly attributed to King Solomon and Kohelet is ascribed to a king in Jerusalem, traditionally understood as King Solomon. While modern scholars do not accept the historical accuracy of these ascriptions, rabbis certainly didn't doubt them. Being ascribed to an ancient king certainly helps if you want to be part of the Bible!
Secondly, Shir Hashirim merited a metaphorical interpretation. The love story was not between a man and a woman but rather between the people of Israel and God. It is this metaphorical, mystical and at times erotic poetry between God and Israel that causes Rabbi Akiva to call it the holiest book.
And while Kohelet does express deep skepticism concerning justice in the world, it ultimately ends with the famous verse, "The sum of the matter, when all is said and done: Revere God and observe His commandments! For this applies to all mankind." The rabbis too certainly would have ascribed to this directive.

מגילה שכתוב בה – that is to say a writing sheet [which contains several columns] of a Torah scroll, since eighty five letters were written in it, it became sanctified and defiles the hands.

Kohelet does not render the hands impure. This is because its wisdom is [King] Solomon's, and was not said through divine revelation:

כדברי בן עזאי כך נחלקו וכך גמרו – and this is the Halakha.