The act of sending someone away or firing them is dismissal. Your friend's dismissal from the pizza place where he kept dropping the dough on the floor means he's looking for a new job — preferably not in food service.
When a school bell rings at the end of the day, signaling that students can leave, that's one kind of dismissal. Bad news from a boss that the company is laying you off is also a dismissal, and when a judge rules that a trial is over and the case has been dropped, it's yet another kind of dismissal. The word comes from dismiss, "send away," from the Latin root dimittere, "send different ways" or "break up."