We learned earlier in the Masechet (tractate) that a father has the ability to accept kiddushin (engagement) for his daughter while she's a na'arah, that's between 12 and 12 and a half years old, and also as a ketanah, which is under 12 years old. We'll talk now about this Mishnah: if a father accepted kiddushin for his daughter but doesn't remember who the man was who accepted it.
The Mishnah says, If a man says, I accepted kiddushin for my daughter, but I don't remember who was the man who accepted the kiddushin for her. I don't know who she's engaged to. Somebody shows up and says, I'm the guy who got engaged to her. We believe that person. We assume that if somebody shows up, he's talking to the father himself. He's not going to be so brazen and lie to the father in his face. The father may remember and say, no, you weren't the guy and know that he was lying. So therefore we make the assumption that this person is telling the truth and he's allowed to marry this woman. If they never figure out who the guy was, this young girl is an eshet ish. She's a married woman and she is prohibited for the rest of her life until she actually gets a get (bill of divorce) from the guy who she was engaged to. If the father never remembers, she's never allowed to marry.
Ah, but in the situation where two people show up, Zeh omer ani kidashtiah (I'm the one who was engaged to her), one guy shows up and he says, I'm the one who was engaged to her. And another person shows up and says, I'm the one who was engaged to her. She's not free to marry another person until she gets a get from both of these men. If they want to, one of them can give a get and the other one can marry her. Even though one of them here is for sure lying, we make the assumption that one of them is also telling the truth. It's more likely that one of them is telling the truth out of these two than both of them lying and she's married to a third person. So therefore, we say if both of them want to give her a get and divorce her, we're going to assume that one of them was the guy that was actually married to her and she's now free to marry a regular person, someone who was not involved in this situation.