When a conventional toilet is flushed, water from the tank rushes into the bowl through an orifice called the flush valve.
Before you trip the lever, this valve is plugged with a rubber stopper, called a tank ball, flush valve seat ball, or the newer, more effective flapper or flapper ball.
The valve and the flapper together are called--not surprisingly--the flapper valve. Tripping the lever simply lifts the rubber flapper off the valve and... whoosh! A flush valve is 2 1/2 inches in diameter--and so is the ball-shaped part of a flapper. The flapper hinges onto the vertical overflow pipe that's next to the valve and a small chain connects the flapper to the trip lever.
The advantage of a flapper over the earlier stoppers is that it doesn't have as many parts to foul or get hung up, so it's less likely to let the tank "run" or leak into the bowl.