Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines.
In simpler words, parallax is a visual effect you experience when moving. Objects closer to you appear to move past more quickly than objects that are farther away. For example, when riding in a car, if you look out the side window, a tree by the side of the road will move through your field of vision much faster than a barn in the distance behind it. This effect is utilized within software to convey a sense of depth.
The most recent incarnation of the Foursquare iPhone App employs a parallax effect in which information on the screen scrolls on a plane above the map.
This GIFF doesn’t do it justice, of course, but a still image wouldn’t convey it at all. The effect is purely aesthetic, but it feels good. It’s an enjoyable microinteraction.