A squirtbox is a cardboard box that is taped shut with a hole cut into it that one would use to masturbate into. This could have a picture of someone's face/genitals taped to it to add to the affect.
"Hey Jim, where's your squirtbox? I need to crank one out!"
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.