I liked the explanation Steven Pinker gave in How the Mind Works: the problem of converting two 2-D arrays of color values into a 3-D model, the problem that the visual system tries to solve, is in fact an unsolvable problem: any given dataset has multiple solutions. On top of this, the visual system has to solve this problem in a finite amount of time, making it doubly-unsolvable.

So the brain makes assumptions about the world that, if true, make the problem tractable: Objects are usually three-dimensional. Adjacent spots on an object tend to be of the same color and brightness. Objects are lighter on the side the sun shines on, and darker on the other side. Objects retain roughly the same shape from one moment to the next. An object moving from A to B will pass through the intervening points. And so on.

Illusions, says Pinker, are drawings cleverly designed to violate one or more of these assumptions, and thus fool the visual system into seeing something that isn’t there.