It is an enhancement to normal mapping, a form of bump mapping, with elements of parallax scrolling.
Parallax mapping creates the illusion of depth in a flat surface. By doing this, it's possible to achieve greater realism with little impact on the game's performance. Parallax mapping is commonly used in stone or brick textures.
Regular bump mapping uses a special texture. This texture contains data about the roughness of the surface - for instance, the data could indicate that bricks are sticking out from a wall whilst the mortar is recessed into the grooves. This data is used by the game's graphics engine to shade the surface according to in-game light sources. For instance, when the player is carrying a lantern or flaming sword past the wall, the bricks will cast realistic shadows on the mortar.
However, bump mapping has a disadvantage. Because the pixels that make up the surface are drawn directly onto the surface, if the player is looking at the surface from an angle, they can see that the bricks don't actually stick out of the wall. This can reduce the sense of immersion because the player can see that the "brick wall" is really just a flat surface.
Parallax mapping is meant to address this disadvantage. In parallax mapping, the pixels that are supposed to stick out from the surface are drawn at a slight distance from their original position, depending on the position of the viewer. This is ultimately an optical illusion, because the pixels are still being drawn onto the original surface, unlike displacement mapping which actually modifies the shape of the surface. However, it still creates a far more realistic effect than ordinary bump mapping or normal mapping, whilst being significantly faster than displacement mapping.
Parallax mapping was introduced by Tomomichi Kaneko in 2001.
It appears in Fear, Gears of War, Oblivion, Bioshock, Crysis, Fallout 3, Perfect Dark Zero, and Kameo, to name a few.