A camera raw file contains all the data that is captured when the shutter button is pressed whereas a JPEG is compressed and a lot of the data is lost. They are often called digital negatives as they serve the same purpose as the negatives in film photography; they are not ready to be used as the final image, but hold all the information and data needed to produce one. This all means that you are left with a higher image quality which also allows you to have more control and manipulate more parameters than a JPEG. All of the metadata is also still in tact, meaning that the original state can always be referred back to if needed.
So, surely you want to see the difference, right? Well you're in luck.
Step 1: RAW - Photoshop
As you can see, the image has been edited and brightened tremendously without losing quality. This is because a JPEG records only 256 levels of brightness, while a raw file records 4,096 to 16,384 levels. This is what is known as a "bit". JPEG captures in 8bit, while raw captures in 12 or 14bit. Those extra bits allow for more control over the adjustments - brightness, shadows, recovery, fill light, exposure, etc. This will give you best results as the images are easier to edit to just how you want them.