A point where the returner can win the game and 'break' the server's serve. Since the server has the natural advantage (they get to start the point), breaking serve is a big deal. Break points won and saved are key stats in any match. Some players are clinical on break points. Others are infamous for wasting them. Having fifteen break points and converting one is a particular kind of tennis agony.
"Break point. She chips the return low and he nets the volley. Break of serve. The crowd erupts."