Hi, a bump map only gives the impression of a bumpy surface and is really only any good if viewed directly on because if you turn the geometry you can see that the surface is still flat if you know what I mean, Where as a displacement map actually displaces the geometry at render time so the surface really is bumpy and in my opinon better for close up work or animated geo.

A specular map is a map that specifys how shiny an object is in any given part so you can create more realism because no object is perfectly smooth and are very rarely the same specularity all over.
An example of this might be a human face, if you take a look in the mirror you can notice that maybe the end of the nose is more specular, the eye lids where it meets the eyeball certainly and the ears are a little more waxy and specular compared to the cheeks.

Hope this helps a little.