Our minds are able to perceive the world in three dimensions primarily because we have binocular vision.  Binocular vision occurs when two eyes look at the same thing at a slightly different angle, resulting in two slightly different images.  The blue squares above show images of the same block that might be seen by each eye.  It's simple to confirm that we have binocular vision: place your hand a foot in front of your face and alternate closing each eye.  Your hand will appear to jump back and forth.

The slight difference between the viewpoints of your two eyes is called binocular disparity.  Binocular disparity is the form of depth perception most used by the human brain, and is the most easily manipulated for perception tasks. The brain is able to take these two different views and mold them together to form a cohesive, three dimensional object.

This picture shows how binocular disparity has often been used in comic books, magazines, and movies.  The picture contains two images of a chair, one red and one blue, from two slightly different angles.  You can "see" the image by putting on special 3D glasses.  One lens of the glasses will filter out the blue image, and the other lens will filter out the red image. The result is each of your eyes is only receiving one of the two images on the page.  Just as if you were looking at a real chair from two different angles, your brain forms these images into one three-dimensional image.