A checked swing is a motion that a batter can make while at the plate. It occurs when a batter starts to swing at a pitch, but changes his mind mid-swing and attempts to pull the swing back. Usually, a checked swing occurs because a batter initially believes a pitch will pass through the strike zone, only to realize that it will not.
If the pitch crosses the plate through the strike zone without contact from the batter, it counts as a strike, regardless of whether or not the batter managed to check his swing in time.
When the pitch does not pass through the strike zone, however, a checked swing could prove the difference between a ball and a strike. If the umpire determines that the batter checked his swing in time (and assuming the batter does not make contact with the ball), the pitch gets called a ball. However, if the umpire determines that the bat broke the plane of the front of the plate, then the motion is considered an attempt to swing at the pitch, and therefore, the umpire may call a strike.
The home plate umpire usually makes the call on whether or not a batter checked his swing before it passed completely through the strike zone. In some cases, the home plate umpire or the catcher might appeal to the first or third base umpire for a call.