Original: As the climber moves on the climb, the belayer must make sure that the climber has the right amount of rope by paying out or pulling in excess rope. If the climber falls, then they will free-fall the distance of the slack or unprotected rope before friction applied by the belayer will start to slow their descent.
Simplified: If the climber falls, the device lets the belayer also hold the rope still, so the climber hangs in the air but does not hit the ground.