From BR Bullpen
A checked swing or check swing occurs when a batter begins to swing at a pitch, but stops in the middle of his gesture, realizing that the pitch is out of the strike zone. The umpire then needs to rule whether the batter interrupted his swing in time, which is usually determined by whether or not the bat crossed the plate. Often the home plate umpire does not have the best view of such a play, and will ask for help from his colleagues at first or third base to make the call. The batter or the catcher can also ask the umpire to seek the help of his colleague, although the umpire may decline to do so. When the umpire does ask for the help, the ball or strike call is said to have been made "on appeal".
If the umpire rules that the pitch did in fact cross the strike zone, the question of whether the swing was checked or not is moot - the pitch is a strike. Similarly, if a batter attempts to check his swing but still makes contact with the ball, the result is treated like any other batted ball.