The backs and sides of virtually all guitars are made of hardwood. Strange as it may seem, softwoods just don't bend well and are more difficult to form into guitar sides. And there is the matter of tone, too.
Sides just don't enter into the vibrations nearly as much as tops and backs. They define the body shape and support the top and back. The back, however, is very significant. If you don't believe me, just sit and play a full chord with the back held tightly against your stomach, and then with the back held completely away from your body. Hear the difference in the fullness of tone?
Mahogany is the most commonly used hardwood for guitar backs because it's relatively economical, durable, attractive, easy to work and resonant.
Mahogany is customarily stained:
Brown like this, or
Reddish, like this
or left "natural" like this:
Time for a quick disclaimer: I realize that color resolution is not consistent on the Internet, so I'll just assume you can see the difference, but I'll use a few words to describe the colors along the way. Color is only one of the many criteria used to identify woods, so it's best to ask someone with more experience, if you're in doubt about a particular instrument's materials.
Mahogany is just about the lightest weight and least dense of all the hardwoods. A guitar with a mahogany back will tend to be very bright in its treble response, and correspondingly lighter in bass. Greater bass response comes from more dense woods.
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