Mipmapping is a pre-computed texture scheme that tries to solve the problem of texturemap aliasing. When a screen pixel from a textured polygon covers many texture pixels, the pixel should be sampled more than only once (nearest neighbor or bilinearly) to get a "correct" average color. So instead of having a regular texture a mipmap is created. The mipmap level is chosen from the objects distance to the camera, and can be per pixel, per object, bi- or trilinearly interpolated, etc. Mipmapping in its nature does not take perspective projection into account.
The 1-channel mipmap texture usually is divided into four parts, holding Red, Green, Blue in the first three, while the last is divided into four parts, holding the downsampled 2x2 average of R, G and B, and so on recursively until a pres-elected depth. I'm sure google has pictures of this.