A clear distinction should be made between 3D textures and mipmapped 2D textures. 3D textures can be thought of as a solid block of texture, requiring a third texture coordinate r, to access any given texel. A 2D mipmap is a series of 2D texture maps, each filtered to a different resolution. Texels from the appropriate level(s) are chosen and filtered, based on the relationship between texel and pixel size on the primitive being textured.
Like 2D textures, 3D texture maps can be mipmapped. Instead of resampling a 2D layer, the entire texture volume is filtered down to an eighth of its volume by averaging eight adjacent texels on one level down to a single texel on the next. Mipmapping serves the same purpose in both 2D and 3D texture maps; it provides a means of accurately filtering when the projected texel size is small relative to the pixels being rendered.