A mipmap is a chain of progressively less detailed textures, used as a computationally low cost way of improving the quality of rendered textures.
The less detailed textures are used when the object or surface being textured is at a distance and the more detailed textures are used as the distance decreases.
Mipmaps are numbered in descending order from smallest to largest, thus level 0 is always the largest mipmap.
A mipmap does not have to be square and no mipmap level may have a dimension less than 1.
Each mipmap level is a power of two smaller than the last one.
Thus a typical mipmap chain may consist of a series of surfaces with dimensions like this:
Level 0 - 64 by 32
Level 1 - 32 by 16
Level 2 - 16 by 8
Level 3 - 8 by 4