Here the Mishnah presents a new case: a woman who comes forward on her own and testifies that she was taken captive by gentiles. The very fact of captivity raises a concern that she may have been violated by them, and consequently she would become forbidden to her husband if he is a kohen, or she would be unable to marry a kohen.
"Nishbeisi u'tehorah ani - ne'emenes" - "I was taken captive but I am pure - she is believed":
Alongside her admission that she was taken captive, the woman adds that she remained pure, and that they did not have their way with her and she was not violated by a gentile during her captivity. In this case she is believed, since our entire knowledge of the captivity rests on her own words. This is the principle of "the mouth that forbade is the mouth that permitted": since we have no knowledge of the prohibition except from her, from her we also learn the permission.
"Im yesh eidim shenishbeis v'hi omeres tehorah ani - einah ne'emenes" - "If there are witnesses that she was taken captive and she says I am pure - she is not believed":
When the fact of the captivity is known from another source, from the testimony of witnesses, her claim of purity is no longer believed, for the mouth that forbade is not the mouth that permitted. Under these circumstances the assumption is that they had their way with her, and she becomes forbidden to the kehunah - and even though it was done against her will, that is enough to forbid her to a kohen.
"V'im mishenisses ba'u eidim - harei zo lo seitzei" - "And if the witnesses came after she had already married - she does not have to leave":
This refers to a woman who testified about herself that she had been taken captive and claimed that she was pure, and on the strength of her credibility she married a kohen, and only afterward witnesses came and testified about the captivity. On the face of it, one might argue that the situation is now as though her claim of purity had never been accepted at all, so that she is forbidden. Nevertheless the Mishnah rules that she does not leave - we do not remove her from her husband, and she remains in her marriage.
The Gemara explains that this leniency is not limited to a woman who has actually married. Even if she has not yet married, but beis din permitted her to marry a kohen, she does not lose that status: since she was established as fit for the kehunah, the later arrival of witnesses does not change her status.
The reason for the leniency according to the Rambam:
Some explain, based on the Rambam, that with regard to a captive woman the Sages adopted an extra measure of leniency, since the entire prohibition is nothing more than a doubt - a doubt whether she was violated by a gentile. And the Rambam holds that the very obligation to be stringent in a case of doubt regarding a Torah law is itself only rabbinic, and is nothing more than an enactment of the Sages. Since the stringency itself is of their making, they had the power to be lenient in circumstances where they saw a need - and for this reason she retains the permission to marry a kohen, or to remain in her marriage to him.