A bump map is a simple image that, depending on its varying color (or shade, usually), is processed into a bumpy surface on an object. Using one doesn't generally provide the precise visual quality of actually modeling the object to have the bumps directly in it, but it severely reduces the amount of overall video processing that's needed for the effect and the amount of physical disk space needed to store the object.
I'll steal a bit from Wikipedia to explain it.
Take this simple sphere:

add this bump map to it:

and get this resulting object:

It takes much less space overall to store a single-mathematical-equation-generated sphere and a picture than it does to have a shape with thousands of mathematically derived dents in it, is all.

That's my understanding.