In short, JPEG is a compressed and processed file. When you shoot in JPEG, your camera only saves a portion of the "information" or quality it can capture to save room for more images (Note: the amount of compression of quality is dependent on the type of JPEG you tell your camera to shoot in). Furthermore, between the time you click the shutter and your image is saved to your memory card, in JPEG the image is "developed" or changed to some extent. The images saturation, contrast, and sharpness is often modified for fast processing. This is often problematic because such a change cannot be undone after the fact.
RAW on the other hand is untouched and stands in its full file. As the name suggests, the camera file is raw, meaning nothing is done to the image itself. This doesn't mean the image can't be altered in the future, but rather in the second of the shot no part of the image is changed. Another distinction between RAW and JPEG, is that in RAW all the information that can be possibly recorded is saved. This causes slower image processing and less room for further pictures (RAW can take up to 4x as much space as a JPEG file).
Now we will the compare the pros and cons of each format: