Gimp (GNU Image Manipulation Program) is a basically a Photoshop freeware clone--bitmap editing with layers, filters, etc. It doesn't have Illustrator-like vector features.
If you already own Photoshop and are comfortable using it, there's really no reason to use Gimp. I'm like both programs, but prefer Gimp, probably just because I've used it longer. I also like the Gimp because it is free and available for many different operating systems.