Manual Mode. The M could also stand for "Man, you better know what you're doing." Actually, working in Manual mode can be a great way to learn about the basics of exposure, because you have the instant feedback of the LCD to teach you exactly what a modification to the shutter speed or aperture will do to your pictures. Manual mode will teach you, very quickly, how apertures and shutter speeds affect your pictures.
Program or Auto Mode. The polar opposite of Manual mode, Program controls both aperture and shutter speed automatically for you. What do you learn? As you can't set specific settings like shutter speed or ƒ/stop, it teaches you to only use Program mode when you really don't care what F/stop and shutter speed you use. That should be a fairly infrequently—particularly if you're trying to improve your photography.
Aperture Priority. This mode is best for when you want to minimize or maximize depth of field, which can be really useful with portraits and product photography. With portraits, you might want minimal depth of field to put the focus on the subject. With product photos, you might want greater depth of field to ensure all of the subject is tack sharp. What do you learn? That a smaller aperture number creates a bigger opening and a shallower depth of field. A smaller opening, corresponding to a larger aperture number, increases depth of field. And you'll also learn how to compensate to create an equivalent exposure when the camera adjusts the shutter speed accordingly.
Shutter Priority. Best for when you want control over the shutter speed, Shutter Priority lets the camera automatically adjust a corresponding appropriate aperture. When would you want to adjust the shutter speed but not the aperture? When you want to stop something moving fast—like for sports or wildlife photography—or when you want to use a long shutter speed for motion blur or at night. What do you learn? When photographing fast moving objects or when you want to create a motion blur, the shutter speed is the most important modifier you can use.
Portrait Mode. The Portrait setting works a lot like Aperture Priority, but it defaults to a wider aperture for a softer background. From that, you can learn that maybe your portraits would look better if you used a wider aperture for a shallower depth of field and a softer background.
Sports Mode. The Sports or Action mode works a lot like Shutter Priority mode, but with a fast shutter speed set by default. This faster shutter speed is used to stop fast-moving objects—like athletes. So any time you want to freeze motion, you should use a faster shutter speed like this mode taught you.
Landscape Mode. The Landscape setting works in exactly the opposite way of Portrait mode. It's a lot like Aperture Priority, but this time with a smaller aperture set for greater depth of field over a wide scene. The smaller the aperture, the more area will be in focus—and that can be crucial when you're photographing a large landscape.
Night Portrait Mode. This mode combines a longer shutter speed (in order to register an exposure in a low level of ambient light) with a flash (which illuminates the foreground subject and keeps them sharp). This mode is a favorite because there's so much going on, and because it teaches you tons about the way photography works. With a long shutter speed, only the ambient light is increased while the effect of the flash stays the same. This way you can balance a strobe exposure with an ambient exposure—a great way to add context to portraits. The combination can be amazing.