This is a topic that most often comes up in my DSLR classes. There are pros and cons to both and sometimes it makes sense to shoot jpegs, sometimes RAW. Hopefully the following information will help you decide which is best for you and under what circumstances.
The main difference between a JPEG and RAW file is that a JPEG file is processed "in camera" by your camera’s processor and a RAW file is processed by "you" using a software program.
Now just because the RAW file is not processed in camera does not mean you can't see it, the camera will render a JPEG version of the file so on playback in camera you can see the image with all of its information.
When JPEG files are processed in camera, in addition to information like ISO, WB and exposure if the camera has a "picture style" that information will be applied. For instance, you can set a camera’s picture style to "vivid" which means that the saturation and contrast will be boosted, or monochrome which will make the photo black and white. Refer to your owner’s manual to see what pictures styles your camera has and how it will affect the image.
The JPEG file can be edited post process using a variety of programs. However, the only way for you to non-destructive editing is to use a program like Adobe Photoshop PSE or CS6 so that you can add adjustment layers and thereby leave the original JPEG file intact. This is not to say that you can't edit a JPEG file in other programs, just that you will get optimum results using a non-destructive editing program.
A JPEG file can be compressed and can be read by any computer program and is a universal file format. These files are the ones we email and share on websites and use in social media. The JPEG file is the default setting on all cameras. Be sure to check to see what the "quality" of the file is that is being recorded. This maybe be designated as "fine", "normal" and "basic". The "fine" option is the best quality as it has no compression on the file and is therefore the largest of the three.
The RAW file is not processed in camera and therefore requires download into a program that will allow you to fine tune the file. Programs that can read the RAW files include but are not limited to, Adobe Photoshop PSE, CS6 and Lightroom. These programs have a RAW processor that allow the user to make non-destructive adjustments to WB, exposure, contrast, saturation and a multitude of other aspects of the file.
The RAW file is a huge uncompressed file that will give the absolute best quality for your images. The drawback is that because it is such a large file it takes up more room on your card and in your computer. That it why it is imperative that you create a workflow in which you delete files to keep your computer running efficiently. See post "Organizing Your Photos".
So which file format is for you?
If you have a program that can process the RAW files, you aren't concerned about space and you don't mind the extra post processing time, the the RAW file is the way to go. A RAW file can always be saved as a JPEG file in the event you want to share it, post it or otherwise. With a program like Lightroom it makes the processing and handling of RAW files a piece of cake. See post "What is Lightroom...."
I shoot RAW files exclusively because it is the highest quality file I can get and it allows me so much more latitude when editing. It is the closest you can get to working in the darkroom.