To play with a guy's balls. The girl can mouth them or handle them with her hands. It is a sexual foreplay which is done to induce a trusting relationship. Once conquered this trust exercise, the man has proven to trust the girl with his most vulnerable body part.
Joey: O Monica, you're good at hand ball; I hope Chandler doesn't find out.
Monica: O don't worry, he's cool with it; I've given him plenty of hand ball.