There are several ways to create the illusion of bending a spoon, some of which involve simple brute force. That isn't the smart way to do it though - the more skilled musicians use simple misdirection and sleight of hand.
As soon as the spoon is in their hand, they push a small piece of silver between their fingers where the spoon's handle should be. That way, they can move the 'handle' to seemingly impossible positions and then back again.