I think it's to do with binocular vision...as in each eye sees something different (try it, concentrate on a pen or something on your desk and wink...it 'changes places' right?) and for the magic eye to work the visual pathways into the brain get confused and so you see the image, from each eye, seperateley.
When you just look at it, it looks a pattern, but then you trick your brain, by going cross eyed or looking for ages, it gets confused and you see the 3d image.