Motion parallax is a depth perception cue, in that when an observer is moving, an object which is closer will have a greater apparent angular speed than an object which is farther away.

(Static) parallax, or binocular disparity, is the effect that objects far away have little difference in angular position from the two eyes whereas objects nearer have a greater difference in angular position. (If you look at something due North of your right eye, the left eye sees it as being slightly East of North.) Motion parallax, then, is essentially the same effect - except, instead of having two static viewpoints, there is one viewpoint moving between two places, and instead of having difference in angular position, there is difference in angular speed.

Angular information regarding the position of an object is one of the strongest of the depth cues. I was in a car once, and I saw a tree in the distance that looked for all the world as if it were closer than some of the landscape occluding it. It caught my attention, and I soon figured out it was standing upright in the back of a truck that was driving in the same direction on a parallel road that was just out of sight. The effect was very confusing because I did not see the truck, so my natural assumption was that the tree was rooted to the ground - however, the apparent angular speed of the tree was much less than the surrounding landscape because it was in fact moving the same direction as I was, so it appeared to be closer. It was quite a disconcerting sight, at first.