Our Mishnah deals with a man who betroths a woman on a condition, and afterward it emerges that the condition was not fulfilled. Two cases are discussed: a condition that she has no vows upon her, and a condition that she has no blemishes.
The condition that she has no vows:
One who betroths a woman "al menas she'ein aleha nedarim" - on condition that she has no vows upon her - and it turns out that she does have vows upon her, this is not a valid betrothal, since the betrothal was made conditionally and the condition was not fulfilled. The vows referred to here are those vows listed by the Gemara, the kind that a husband typically minds and is sensitive about.
He married her without restating the condition, and afterward vows were found:
If, after making this condition at the time of the betrothal, he married her without restating the condition, and only afterward the vow came to light, the Mishnah says "teitzei shelo bikesubah" - she goes out with a get, but she does not collect her kesubah. The Gemara explains both sides of this ruling:
The need for a get: Since he did not restate the condition at the time of the marriage, we suspect that perhaps he is no longer insistent upon it. And when he lived with her after bringing her into the chuppah, it is well known that a person does not want his relations to be considered relations of promiscuity, an act of licentiousness that lacks the purpose of marriage, and therefore he intends that this act serve as an act of betrothal. It emerges that even if the original betrothal never took effect because of the condition, it is possible that a new betrothal took effect at the time of the marriage, and therefore she requires a get.
The exemption from the kesubah: Regarding money, the husband can claim that he still stands by his condition: I stipulated a condition at the outset, and I need not repeat it. The get is given only because of a doubt, lest she be a married woman; but with regard to money he claims that this was a mistaken transaction, that the condition was not fulfilled and there is no betrothal here, and therefore he is not obligated in the kesubah.
The condition that she has no blemishes:
One who betroths "al menas she'ein bah mumin" - on condition that she has no blemishes - "venimtze'u bah mumin" - and blemishes were found on her - before the marriage, this is not a valid betrothal, for it was made conditionally and the condition was not fulfilled.
The same law applies where he married her without restating the condition: if after the betrothal he married her without repeating the condition, and afterward blemishes were found on her, "teitzei shelo bikesubah" - she goes out without a kesubah. This is for the very same reasons: she goes out with a get, because of the concern that perhaps he betrothed her through relations at the time of the marriage, since a person does not want his relations to be relations of promiscuity; but he is exempt from the kesubah, since he claims that he stood by his condition, and since the condition was not fulfilled she is not married at all.
What is considered a disqualifying blemish in a woman?
"Kol hamumin haposlin bekohanim poslin benashim" - all the blemishes that disqualify kohanim disqualify women as well. All those blemishes listed by the Gemara in Maseches Bechoros, on account of which a kohen is disqualified from serving in the Beis HaMikdash, are considered blemishes in a woman as well with regard to this condition.
In summary: In both cases - the condition that she has no vows and the condition that she has no blemishes - if it became clear before the marriage that the condition was not fulfilled, there is no betrothal at all. And if he married her without restating the condition, she goes out with a get because of the concern that perhaps he betrothed her through relations, but she does not collect a kesubah, since with regard to money the husband can stand by his original condition. The definition of a blemish is derived from the blemishes that disqualify kohanim from the service.