in really really really simple terms it works SOMEWHAT like this...
when you get a cut, what happens? your skin heals at the spot of injury and creates a scar, which is many times stronger and more durable than the original skin.
in a way, rebuilding stronger muscles is your body's way of insuring that the breakdown and destruction of muscle fibers (lifting) wont happen again.
again this is a very very basic and simple analogy.