Parallax scrolling is an extremely nifty effect seen mostly in 2D games. It gives a three-dimensional feel at little performance expense; this made it used in nearly all 2D games. Parallax scrolling works on the idea of perspective - objects far away will not move as fast as objects nearby. The scene is divided up into different layers-a bitmapped foreground, background, etc. The closer the camera is to a layer, the faster that layer will scroll, while distant objects like the background will move slowly. Thus, this technique creates the illusion of depth commonly seen in 2D games.
Sonic the Hedgehog 3 deserves special mention for showing what exactly is possible with parallax scrolling. In Icecap Zone, lots of middle grounds are used, with little windows in the background giving the player a small view of the outside world. Hydrocity Zone took it to the extreme; the player's perspective of the water surface would actually change if the player was above or below water. All in all, it's an important part of 2D programming.