Commentary for Berakhot 2:1
הָיָה קוֹרֵא בַתּוֹרָה, וְהִגִּיעַ זְמַן הַמִּקְרָא, אִם כִּוֵּן לִבּוֹ, יָצָא. וְאִם לָאו, לֹא יָצָא. בַּפְּרָקִים שׁוֹאֵל מִפְּנֵי הַכָּבוֹד וּמֵשִׁיב, וּבָאֶמְצַע שׁוֹאֵל מִפְּנֵי הַיִּרְאָה וּמֵשִׁיב, דִּבְרֵי רַבִּי מֵאִיר. רַבִּי יְהוּדָה אוֹמֵר, בָּאֶמְצַע שׁוֹאֵל מִפְּנֵי הַיִּרְאָה, וּמֵשִׁיב מִפְּנֵי הַכָּבוֹד, בַּפְּרָקִים שׁוֹאֵל מִפְּנֵי הַכָּבוֹד, וּמֵשִׁיב שָׁלוֹם לְכָל אָדָם:
If one were reading [the section of the Shema] in the Torah and the time for the recital [of the Shema] arrived — if he concentrated, [According to the view that mitzvoth require intent, "If he concentrated" is understood as: if he were intent upon fulfilling his obligation; and according to the view that mitzvoth do not require intent it is understood as: if he concentrated upon reciting it with the correct vocalization (as opposed to reciting it for proof-reading purposes, where he does not read the words as they are vocalized, but as they are written in order to discriminate between defective and plene forms, in which instance he does not fulfill his obligation). And we rule that mitzvoth require intent.], he has fulfilled his obligation, and if not, he has not fulfilled his obligation. Between sections ["Between sections" is explained later in our Mishnah.] he extends greeting out of honor [He extends greeting to one whose honor warrants it, such as his father, or his teacher, or one superior to him in wisdom], and he returns greeting. [It goes without saying that he returns greeting to them if they greet him first.] And in the middle [of a section], he extends greeting out of fear [i.e., where he is afraid that the other might otherwise kill him. And it goes without saying that he returns greeting to him. But he may not do so out of honor], and he returns greeting. These are the words of R. Meir. R. Yehudah says: In the middle [of a section] he extends greeting out of fear, and returns greeting out of honor [i.e., in deference to one it is incumbent upon him to honor]. Between sections he returns greeting to all men [who greet him. And the halachah is in accordance with R. Yehudah. And wherever it is forbidden to interrupt the recital, it is forbidden to speak in the holy tongue as in any other language.]
Bartenura on Mishnah Berakhot
English Explanation of Mishnah Berakhot
In the breaks [between sections] one may give greeting out of respect and return greeting; in the middle [of a section] one may give greeting out of fear and return it, the words of Rabbi Meir.
Rabbi Judah says: in the middle one may give greeting out of fear and return it out of respect, in the breaks one may give greeting out of respect and return greeting to anyone.
The first section of this mishnah deals with having proper intention when reciting the Shema. The second section deals with interrupting reciting the Shema to greet someone.
Section one: Someone is reading the Torah and he just happens to read the portions of the Shema at the time in the morning or evening when he is supposed to recite the Shema. While this may seem extremely unlikely since the Shema’s three portions are not found consecutively in the Torah the mishnah is teaching a lesson. Merely reading the Shema as if one is simply reading from the Torah is not sufficient to fulfill one’s ritual duty to recite the Shema in the morning and in the evening. One must recite the Shema with the intention in mind of fulfilling one’s obligation to perform this mitzvah. Only if one has such an intention in mind, has he fulfilled his mitzvah.
Section two: This section deals with being forced to interrupt someone to offer a greeting. It seems that in ancient times people took greetings far more seriously than we take them today. Not greeting someone properly was considered a serious insult. Therefore, both Rabbi Meir and Rabbi Judah allow certain interruptions in the recitation of the Shema in order to greet people. Rabbi Meir rules more strictly. In between the paragraphs one can greet and respond to someone to whom one owes respect. In the middle of a paragraph one can interrupt but only to greet or respond to someone whom one fears, such as a king or other powerful official. But one should never interrupt just to greet an ordinary person and in the middle of a paragraph one may interrupt only out of fear and not out of respect.
Rabbi Judah is more lenient on each count. In the middle of a paragraph he may initiate a greeting out of fear (Rabbi Meir agrees with this) and he may respond to one even out of respect (Rabbi Meir says only out of fear). In between paragraphs he may initiate a greeting out of respect (this agrees with Rabbi Meir) and he may respond to anyone (Rabbi Meir disagrees).