If you play old games that have 'blurry' textures, you can try forcing trilinear to see if it helps. If you just leave it at off, all remotely modern games will either select trilinear or let you set it in texture options. I believe, 95% of the time, trilinear is used if you select anisotropic. Actually, it's usually a combination of both where bilinear is used way farther down the road (no pun intended).
To answer your question, mipmaps are different stages of texture filtering. You'll notice them easiest when you turn off AF and look at a floor. There will be clear stage(s), then blurry stage(s). This is to help make the game run at a reasonable speed. Some games allow you to color code the mipmaps with a command.
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