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Camera raw is a format that your camera records pictures in just like .jpg does only without compression and with the ability to recover much more information.

Your cell phone records its images using the .jpg format.  .jpg is great because the file size is small and it is easy to upload to the web.  The downside is that you lose quality and the ability to modify the images very much.

The best way to see this is to look at the following images:

Here is the original image (the raw and .jpg look exactly the same right out of the camera).

Here is the best color correction that can be achieved starting with the .jpg image:

Here is the color correction starting with the raw photo:

As you can see the raw image has a lot more leeway for correction.

This is a pretty extreme example.  Normally, a good photographer would be able to get a much better exposure to start with, but if you’re paying top dollar for important photos, shooting raw images is mandatory for maximum quality and versatility in post production.