Originally Posted by shakran

Easy explanation:

Ever take a bucket of water and swing it around really fast? The water stayed in the bucket even when it was upside down because of centrifugal force. The theory behind the space elevator is the swinging bucket on a massive scale. run a rope from the earth way out in space. The rotation of the earth swings whatever's on the end of the rope really freakin' fast. The centrifugal force makes your end-of-rope object pull tightly on the rope, which allows you to run an elevator car up and down the rope.