Bumpmap textures change the way light affects the given texture.
It often gives the texture a more realistic feeling.
The bumpmaps were said to work again in toribash 4.0.
If you plan on getting a refund for your bumpmap purchase, you won't.
Try selling the bumpmap on the forums, IRC, or ingame.
(Junibug: Nuthug isn't even wearing bumpmaps.)