mipmaps are just scaled versions of the same texture, i.e. a basic 256x256 texture will look pretty silly if it's all the way across a large map, versus being right up against your face.
Therefore, they scale the texture into different "mipmaps", a 256x256 (the main one), a 128x128, a 64x64, a 32x32, etc.
Then, the textures will be rendered using the appropriate mipmap, depending upon the "distance" the texture is from you.
As you can imagine, there can be very obvious delineations where the mipmaps change. The easiest way to notice this is to stand on a large floor in a game like Quake3. Look at the floor, as the floor moves away, there will be a noticeable "line" of blurriness where it seems that there is a very definite change in texture quality. that is the mipmap line.
trilinear filtering is a method of blending mipmap delineations so that they aren't so annoying
it's somewhat effective, high-tap anisotropic filtering is another way, mipmap dithering is another way.
typically, high-tap (large # of samples) anisotropic filtering is considered "best", but comes at a hefty performance hit. The Geforce cards have a unique method of trilinear filtering which allows for trilinear to be enabled with a very minimal framerate loss. This is, IMHO, the best feature the GeForces have.
now that I'm done, watch my explanation get torn up for being technically off. <g>