Batcaver seems to be an old localized term for goth. It was used in the Pacific Northwest in the 80s but on the East coast, few people have heard the term. The singular batcave was also used.
I went to a Bauhaus concert last week and it was full of batcavers.
It is said of the situation where a person has the bad luck to make contact with his testicles against an undefined surface or object, intentioned or not.
Given the nature of the word, it is more appropriate to design cases where the interaction is made with a moving object, for example, a ball.
Although it is extremely painful for the victim, it tends to be considerably funny to people who witness it.
Today in the baseball game the pitcher took a nutshot; the baseball hit him in the nuts.
Man, I just watched the funniest nutshot video ever.