Some folks here have mentioned better
dynamic range as a good reason to shoot RAW. Another good reason that doesn't get much lip service is
gamut. Put simply, gamut is the range of colors that a device can reliably reproduce.
Most imaging devices bake jpegs into the
sRGB color space, which is sort of the least-common-denominator for color reproduction between digital devices. The range of colors it describes is quite limited compared to what a camera sensor records.
Higher-end digital cameras can also squeeze jpegs into
Adobe RGB, which is sort of a standard "better" working space. It's not too bad, but (like everything else when shooting jpeg) you're limited to the particular tone curve your camera used to squeeze its native sensor data into Adobe RGB at the time of the shot. If Adobe RGB can't describe a color at the time the image is made (& I should add, with the camera's white balance setting at the time), then it will be dealt with in whichever way the camera deals with out-of-gamut colors (my guess is that it's probably
perceptual which means that there's not a lot of clipping going on, but also that color reproduction isn't particularly accurate. I've certainly never seen a camera jpeg engine with selectable rendering intent...).
Most RAW converters (including Adobe) use
ProPhoto RGB as their native working space. This means that *all* the color data from the camera sensor can be accessed & manipulated by the RAW converter, and you can choose your preferred rendering intent to squeeze the gamut down to the profile of the destination medium (usually the profile of your printer/ink/paper combination, or sRGB for the web). Adobe has a feature that lets you check for out-of-gamut color clipping for the target profile with your selected rendering intent so you can adjust accordingly.
Basically what all this means is that if you're not shooting RAW, the jpeg engine in your camera is throwing away color data.
BTW, if you're interested in learning more about color management beyond the links above, Bruce Fraser's
Real World Color Management was the book that taught me what I know & how to put it to use. It's considered to be the authoritative guide on this stuff by a lot of professional photographers.