Name stems from what actually happens at the ball: the daughter pledges (gives) her virginity to her father, who then gives it to her soon-to-be husband on her wedding day.
If you don't really understand the concept of incest, look it up.
Megan: Yeah. Didn't she go to a purity ball last Thursday with her dad, or something?
Katie: Haha, you mean the Incest-Fest last week? Yeah.