This is similar to real fog, except that game fog is a perfect gradient, whereas real fog usually has some wispy uneveness to it.
Heavy fogging in a game is used to disguise the far clipping plane, as here in the game Turok. In fact, you can see the polygons being clipped, just behind the monster's head. This fog isn't done well, instead it should completely hide the clipping plane. Besides, heavy-fogging is generally looked down upon, because it shortens the distance you can see enemies.
In some of the newer game engines, volume fog and ground fog are supported, where the fog is localized to a specific area, which is closer to the behavior of real fog.