The Gemara is discussing the conditions in which there is an assumption of impurity that will prevent a woman from marrying a cohen (priest). Some young women who had been kidnapped and freed were brought to the great yeshiva of Nehardea, for their case to be clarified before the head of the Yeshiva, Shmuel - one of the greatest of the rabbis. And note that the rabbis function as scholars, and as judges, and as leaders of the community. Shmuel's father sent someone to chaperone the young women, to which Shmuel commented that it would seem a bit late for chaperones. His father responded sharply: If they were your daughters, would you be so careless with their reputations?
The rabbi of our daf yomi class says that in his opinion, this is the single most important statement in the entire Talmud.