Okay, you can stop worrying. I think I understand it now. Basically, instead of using a single coloured bump map, the normal map uses a multicoloured image to increase the depth of a model. Generally, the red channel represents the shading of the object from the right, the green channel is the lighting of the object from below, and the blue is the object from front on.
This has the advantages of regular bump mapping - that is, to create a detailed object without using as many polygons - but normal mapping will often create a more detailed effect, with far less processor usage.
