My camera can take save images as both JPEG and RAW at the same time. In this example, the JPEG is on the left and the RAW on the right.
JPEGs save much faster, take up much less space, are usable just as they are, can be opened by just about anything and Windows can automatically display a thumbnail of the image. The biggest drawback of JPEG is that it is a lossy format, and working with a JPEG just makes things worse.
RAW files, on the other hand, contain the unprocessed data directly off the image sensor. They are higher quality, offer finer control, are generally 12 or 14 bit (vs JPEG's 8 bits) and are lossless. The drawbacks are its enormous file size (7 times larger than JPEG on my camera) and a proprietary format that might be difficult to open in the future.
In this particular image, notice the sky is a truer blue, there is more contrast in the clouds, the ground haze is more visible, the tractor wheels and clouds are whiter and the grass a bit greener on the RAW side.