lol, no, not abbreviations but a pronunciation guide, which it turns out is wrong. The word comes from isotropic, with the an- suffix of course meaning the opposite of. So it means "not isotropic". Isotropic means "identical in all directions".
Aliasing is an effect caused by rasterization (the way in which pixels are arranged in a grid) such that diagonal lines appear jagged. Anti-Aliasing smoothes out the jagged edges by making more of a gradient across the edge, such that the color from the background and foreground fade into each other slightly at the edge.
Anisotropic filtering sharpens textures, especially those viewed at a distance or at an angle, although exactly how it does this I haven't a clue.