Gamma correction lets you keep your shadow and highlight levels essentially fixed as you adjust midtones up or down.

Gamma lets you raise the perceived contrast as it is lowered and lower the perceived contrast as it is raised.

On washed out pictures for example dropping the gamma will richen the tone. You can also lower the black levels then play with the gamma to bring back detail. This may not work with video footage that has suffered heavy generation loss though.
If you use a waveform monitor you will see the mid tones go up as you raise the gamma level.

Rarely, if ever should you use brightness and contrast adjustments.

A word of caution:

1. Computer monitors display gamma differently than a TV Monitor. That is why you need an external monitor to do good color adjustments

2. As you raise gamma levels visible NOISE increases. So there is a limit.

John

Despite the large number of filters in Sony I think it is no exaggeration that for run-of-the-mill correction 95% of skilled editors will 95% of the time use ONLY the levels and the primary and secondary color correctors. Play with the third-party Auto Levels filter, it is quite good as it has preset film gammas.

EDIT: I forgot Color Curves from my list!!!! Sorry.

You should also consider using Color Curves. It gives you much more control on exactly which part of the brightness range you need to adjust. I deal with restoring old photographs, and often they look "hazy." Merely stretching the whites and blacks to the endpoints of the histogram often doesn't give you a good looking result because the brightness values near the white and near the black end of the spectrum need to be moved. Gamma operates most forcefully on the brightness values in the dead center (gray). When this is not what you want, you need to use the color curves. For really exacting work, they are the only way to go.

They are also useful for dark video (e.g., wedding video shot at the reception, at night, without additional lighting). If you simply increase the gamma, you'll end up with a gray-looking video with lots of noise. If you instead play with the color curves, you can often keep the shadows fairly dark and noise free (losing, of course, some detail that you might bring otherwise bring out), but still increase enough of the midtones to make the video more watchable. For me, the goal is to make the video easier to watch, while still staying true to how it was shot, and how the scene looked.

These tools do the same thing just as sanders, planers, and lathes all just remove material from a block of wood.

Everyone has given you good advice so I'll just recommend a couple of things.

When you adjust levels, curves, or brightness/contrast, make sure you have the scopes window open. Normally I'd look at the histogram view while making adjustments.

If you ever get the opportunity, do some levels correction in photoshop. The adjustment panels are usually better designed to give you visual feedback.

Shoot a series of tabletop product stills on simple backdrops and then correct them in photoshop. These sorts of photos are visually simple and a good excercise.

There is a good book on color correction for video:
Color Correction for Digital Video by Steve Hullfish and Jaime Fowler

Rob Mack