Debug and Release are just labels for different solution configurations. You can add others if you want. A project I once worked on had one called "Debug Internal" which was used to turn on the in-house editing features of the application. You can see this if you go to Configuration Manager... (it's on the Build menu). You can find more information on MSDN Library under Configuration Manager Dialog Box.
Each solution configuration then consists of a bunch of project configurations. Again, these are just labels, this time for a collection of settings for your project. For example, our C++ library projects have project configurations called "Debug", "Debug_Unicode", "Debug_MT", etc.
The available settings depend on what type of project you're building. For a .NET project, it's a fairly small set: #defines and a few other things. For a C++ project, you get a much bigger variety of things to tweak.
In general, though, you'll use "Debug" when you want your project to be built with the optimiser turned off, and when you want full debugging/symbol information included in your build (in the .PDB file, usually). You'll use "Release" when you want the optimiser turned on, and when you don't want full debugging information included.