RAW is the unprocessed data that your sensor receives. This presents us with several benefits: since the information is encoded in more than the standard 8 bit/pixel of the JPEG format, more tonal information can be extracted. At first this doesn't appear to be anything exciting, until you find out that you can gain up to one stop of exposure by working with levels and curves. This can be crucial in those shots where you can't afford to mess up.
The other important advantage of RAW is that the white balance setting on your camera becomes irrelevant, as you can change the white balance in post-processing applications such as Apple's Aperture, Adobe Lightroom, Silkypix etc.; without losing any detail or colour information.
The downside is that they're huge.
JPEG has none of what I have said above, but it is a considerable amount smaller.
Hope this information has helped. If anybody else has something else to add (or correct me if I'm wrong), please do so.
