In a previous article, Shooting Modes Explained, I went into some of the details of the major shooting modes (aperture priority, shutter priority, manual) and the program modes (what Canon calls “PictureStyles” and Nikon calls “Digital Vari-Programs”).
All of that information is still very important, but I wanted to mention that a good fellow by the name of Adam Parker posted a comment there with a useful link to an article of his where he demonstrates the major shooting modes using… Gasp… Pictures!
You can read his article, Canon Shooting Modes - What Are the Differences? at that link. Bear in mind that it is a very Canon-centric article, and therefore I fully support it!
If you have a Nikon or one of those… Other cameras… This information may still apply, though the names of the modes will probably be different, or you may have more or fewer of them.