Uh oh. Strap yourselves in, boys!
hehe...
You may want to search on this one, there are ENDLESS discussions on this topic.
In short...
JPEG: Camera makes interpretations on the scene based upon what it thinks is appropriate white balance and exposure, and then discards "unecessary" information giving you a compressed image. (JPEG is a lossy compression format) You can make adjustments on the image, but if the data simply isn't there, there is nothing to adjust.
RAW: The camera makes NO interpretations and gives you a complete dump of what the sensor "saw" at the time of exposure. You then make adjustments for exposure and color balance in post-processing on your computer. RAW allows you some 2-4 stops of "error" in exposure without loss of image data, as well as pretty much full color range adjustment without loss.
My personal recommendation is to shoot JPEG until the day you realize that a RAW image would have saved you from a critical error you made, and then start shooting raw for at least those kinds of situations, and possibly all situations. For a lot of people, JPEG works just fine pretty much forever. The more you learn about the craft, the more you realize that RAW is critical in a lot of situations.