Mipmapping uses versions of the texture at smaller & smaller sizes image, to effectively pre-compute the average of many texels.
As a texture gets more and more minified, many texels will correspond to a single screen pixel, and using a "nearest" or "linear" filter will not compute an accurate result. The texture will appear to flicker as the object moves.
A mipmapped texture avoids the flickering problem when minified. As a result, it can look a bit fuzzier.