Gwern recently cited a paper, Attention and awareness in stage magic: turning tricks into research, that describes the neural basis of spoon bending and the dancing bar illusion:
Spoon bending. In this illusion the magician bends a spoon, apparently by using the power of the mind. In one part of the trick, the magician holds the spoon horizontally and shakes it up and down. This shows that the neck of the spoon has apparently become flexible. The apparent rubberiness of the spoon is an example of the Dancing Bar (or Rubber Tree) illusion, in which an oscillating bar (or rubber tree) seems to bend when it is bounced rapidly. The neural basis of this illusion lies in the fact that endstopped neurons (that is, neurons that respond both to motion and to the terminations of a stimulus’ edges, such as corners or the ends of lines) in the primary visual cortex (area V1) and the middle temporal visual area (area MT, also known as area V5) respond differently from nonendstopped neurons to oscillating stimuli. This differential response results in an apparent spatial mislocalization between the ends of a stimulus and its centre, making a solid object look like it flexes in the middle.