A taint is the stretch of skin found only on women between the pussy and the asshole. The term originated from the phrase "taint an asshole and taint a pussy." In contrast the skin between the scrotum and asshole on a man is referred to as the "gooch" and first known usage is a reference to Bob "the gooch" Guccione the owner/publisher of Penthouse. His employees and acquaintances couldn't quite decide if he was more of an asshole or a dick, a general consensus eventually formed that he was both and "everything in between," hence the gooch.
Q: Hey lady, do you know why the piece of skin between your vagina and anus is called a taint?
A: Because it taint a pussy, and it taint an asshole.