When your camera takes a picture, it reads a bunch of brightness values from the sensor. This is the "RAW" data. Your camera can then apply a bunch of transformations on that data to make it viewable. It can adjust the white balance, sharpening, contrast, saturation, and other things. When it is done, it also shrinks the file by throwing away data that it doesn't think you'll use. The end result is a JPG file.
A JPG is great because it can be viewed and printed by almost anything. A RAW file is proprietary. Only your camera company or specialty software can read it.
Shooting JPG is easy because the end result is something that you can use right away. JPG files take up less space on a memory card. You camera can write them faster, so if you are taking lots of shots in a hurry you can take more shots more quickly.
RAW files have advantages as well. If you change your mind about any of the settings, you have more flexibility with adjustments.
Many people use the analogy that a RAW file is like a negative and a JPG is like a print. I've also heard the analogy that a RAW file is like the ingredients and a JPG is like a cooked cake. In essence, you'll pretty much always end up with a JPG. With a RAW file, you have to create the JPG yourself but you have much more control over it.
In the old days when space was expensive and cameras wrote slowly, there was a big split between those shooting RAW and those shooting JPG. With space cheap now, almost every serious shooter shoots RAW almost all of the time. Some exceptions are those on tight schedules (like sporting event shooters) or situations where quality really doesn't matter that much (like your kid's friend's birthday party). RAW files do require special software, so many beginners avoid shooting RAW.
With the exception of a couple of pro sports shooters, I've never met a photographer that has taken the time to learn to process RAW files that has gone back to shooting JPGs for most of their work.