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עשרה יוחסין עלו מבבל – that Ezra set aside all of the ineligibles who were in Babylonia and they were brought up with him, in order that she shouldn’t be mixed with traced genealogies, because there was no Jewish court there.

Ten genealogical classes went up from Babylonia [in the time of Ezra and Nehemiah]: Priests, Levites, Israelites, halalim, converts, freed slaves, mamzerim, netinim, hushlings and foundlings.
Priests, Levites and Israelites may marry each other.
Levites, Israelites, halalim, converts, and freed slaves may marry each other.
Converts, freed slaves, mamzerim and netinim, hushlings and foundlings, may marry each other.
This mishnah introduces a concept that was very important in marital law in the mishnaic/talmudic times and continued to be a prominent factor in the choice of spouse throughout Jewish history: genealogical class. In Hebrew this is called: yichus. There are some genealogical “classes” who may not marry each other (Israelites and mamzerim, priests and converts). As I have stated before, in our modern society it is hard to grasp the importance of such categories in the ancient world. Until recently it was believed that a person is qualitatively reflected in their class; belonging to a social/religious class is an integral part of one’s identity. However, we should realize that in rabbinic halakhah class structure is only legally relevant to choice of marriage, and occasionally to positions of leadership. When it comes to other elements of society, Jews seem to have mingled relatively freely. The rabbis recognized well that a person’s integrity, wisdom and virtue did not depend upon his social class. Nevertheless, it was an important criterion in choosing a spouse.
Section one: The mishnah attributes the separation of the Israelites into ten genealogical classes to the return to Zion from the Babylonian exile in the time of Ezra and Nehemiah. It is clear from the book of Ezra that genealogical lineage was an important issue to the authors of the book and to the leaders of that time period. Ezra demands that the men send away their foreign born wives. In the lists of returning exiles lineages are listed and there are verses which show that priests who couldn’t demonstrate their lineage were denied their priestly rights. In other words, although this mishnah may contain what is basically a legend, in may be based on some historical recollections.
According to the mishnah, which is probably legend, lineage was so important to Ezra that when he gathered up the exiles and brought them back to the land of Israel, he separated them into classes. When they returned to Israel, each person would therefore know their proper status.
Most of the classes mentioned in this mishnah should be familiar by now. Natinim are descendents of Temple slaves, and are actually mentioned in the books of Ezra and Nehemiah (see for instance Ezra 8:20 and Nehemiah 7:62). Halalim are the children of disqualified priests. Hushlings and foundlings will be explained in tomorrow’s mishnah.
Sections 2-4: Here the mishnah lists who may marry whom. Subsequent mishnayot will clarify some of these statements. For now we should note that converts can marry Israelites and can marry mamzerim. Other sages hold that converts may not marry mamzerim. There is also some debate over whether certain types of converts may even marry priests.

חללי – Kohanim who were born from those who had been ineligible for the priesthood, such as a widow [married to] to a High Priest or a divorcee, the female issue of a Kohen’s illegitimate connection (or a Kohen’s wife illegitimately married to him), and/or a harlot to a common Kohen.

חרורי – freed slaves.

נתיני – Gibeonites who were circumcised in the days of Joshua, and were prohibited from marrying into the community [but would serve as water drawers and hewers of wood].

שתוקי ואסופי – we will explain them further on (Mishnah 2).

גיורי וחרורי ממזרין כו' כולם מותרים לבא זה בזה – for a community of converts is not considered a community, and Mamzerim are not warned about that they should not enter the community of converts, but Levites, and Israelites cannot [marry] with a Mamzer. And the illegitimate child of unknown fatherhood and the foundling, whose father and mother are unknown, are doubtful Mamzerim (i.e., illegitimate) and are permitted to be mixed with certain Mamzerim, for we say that into a clear congregation he may not enter, but into a doubtful congregation he may enter.