The difference between raw and jpeg in common sense language.
Raw format contains the image, unprocessed, directly from the camera. i..e no in-camera processing has been applied and pretty much the way the lens saw the scene. The file sizes are enormous and take much longer to store on your memory card after you've taken the picture. Most raw pictures will require some post processing e.g. color saturation, sharpening etc. The main advantages have to do with the fact that you are the one making the decision on how much adjustment to make - not the camera manufacturer.
JPEG format has been altered by the camera's internal software. This includes application of proprietary compression techniques to reduce the file size. Adjustments to various details such as lighting, color, etc.
Each file format has its die-hard adherents. Some cameras now allow you to create a a raw image and a JPEG image at the same time in your camera. you can imagine how long it takes to save these after you've pressed the button. High Speed memory cards are a must.
I suppose the primary lesson to be learned is that it depends on what's your objective. If you are interested in tweaking your own picture settings to the nth degree or you are saving the files for very delicate archival purposes you need to be committed to using RAW images.
For the casual photographer JPEGs are fine. As for myself, I'm 60+ with aging eyes thus JPEGs work fine for me. perhaps if I were more "sightful" and more patient in processing I would take the "raw" route.
Incidentally, by using raw you will either have to use the software that came with your camera or buy other software that is specifically designed to handle "raw" files from your camera.
Hope this helps.