RAW images aren't compressed. What this means is, you're essentially recording what the camera sees, and that information remains there, so when you bring it onto a computer and have software such as Lightroom, you can adjust the settings, colour etc quite a bit without actually affecting the quality. So essentially with RAW's you can repair them a lot easier, where as JPEG's are compressed down so they store less information. Because the computer has less information, repairing it is a lot more harder and a lot of the times JPEG's just can't be repaired.
Also, cameras aren't perfect: they have small imperfections like hot pixels etc. If you shoot RAW, image editing software such as Lightroom automatically fixes them.
Try thinking of it like this:
- RAW: the computer has more information to work with, therefore can adjust the information in a better way to still keep the original quality.
- JPEG: the computer has less information to work with, therefore even though you can adjust things such as shadows etc, it doesn't really know what was actually there and hence can't really fix it.
So if you have more information, you have more chances of fixing it. Because RAW's store more information, they take up much more file size.
Although as stated above, RAW files will need processing on a computer. So takes longer, but in my opinion really worth it. However, some new cameras such as the 60D have built in RAW processing, which means you can process them in camera (would never do this unless was on like a long flight etc).
A lot of photographers use RAW, it's a massive benefit and is a lot safer. I would highly recommend it. Although I did once attend a wedding and the photographer was shooting in JPEG mode (a bit risky in my opinion) but they all turnt out to be perfect. So really, whilst RAW and JPEG are both doing the same thing and getting the shot, a lot of the time it's just a case of "better safe than sorry."
So my advice to you is, if you have software which can process RAW images such as Photoshop, Lightroom etc, shoot RAW. If not, shoot JPEG.
Hope this helps.