Used as a response to point out an unintentional double-entendre in which the original speaker could be taken as intending to perform some act that would be more appropriate for a sex, kink, or other "special" party.
Person A: I'm going down to get a drink of lemonade, do you want some?
Person B: Dude, it's not that kind of party!
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.