Also known as AF, anisotropic filtering is a method of enhancing the surface texture of an object. Where anti-aliasing deals with smoothing the edges of an object, anisotropic filtering deals with what's inside those edges. Anisotropic filtering, like anti-aliasing can have an adverse effect on games performance, even more so when both are used together.
There are commonly three settings in relation to anisotropic filtering. These are bi-linear, tri-linear and full anisotropic. The anisotropic setting is the most powerful setting, but will also give you a bigger performance hit. Settings for anisotropic filtering range from 2x to 16x; the higher the factor of anisotropic filtering the greater and more clear the detail is across a bigger distance of the on-screen display.