A woman's vagina which is unclean, infected, or diseased. It is the type that most men would not want to be involved with.
Alternatively, one might say that they got some "nasty pussy" from a freak
female who is very hot and mean it in a good way.
But usually, it is meant in a bad way.
Man, that bitch has some nasty pussy! I wouldn't touch that with a ten foot pole!
Yo, I got laid last night and it was some nasty pussy, man! That chick is such a freak!