Shooting your photography in raw format is really is worth the trouble.
When making photographs many, maybe a majority of cameras offer the choice of saving the image as a JPEG or a raw image - or both. When saved, JPEGs generally have the extension .JPG, whereas raw files will have different extensions like .CR2 from Canon, .NEF from Nikon, .RAF from Fuji, and in some cases, .DNG for those manufacturers using Adobe's generic format.
The confusion doesn't end there, though. While a JPEG is a JPEG is a JPEG (more or less), a Nikon raw file from my D300 is different from one from my D800, and they share little if anything with a CR2 file from say, a Canon 5DIII.
Happily, it doesn't matter. Companies such as Adobe, Apple, Capture One and Serif wade through the specs and their software can generally work out what's what.
The "problem" with raw is this: it's a bit like shooting negative film instead of Polaroid instant film. In the same way that Polaroids were there in a minute or so, but film required processing and printing, raw files need processing in software like PhotoShop or Photos. (Chances are you have something that can do such processing already on your computer. If you have a Nikon or a Mac, I can guarantee this.) JPEGs on the other hand, are pretty much ready to go as they come out of the camera. And just like Polaroid versus say Fuji Superia, choosing JPEG instead of raw trades convenience for flexibility.
With a Polaroid image, you had an image (almost) instantly, but that was that. You couldn't adjust the image; it was as it came out of the camera. Film on the other hand required processing, but you could do things: crop, change exposure, dodge and burn, etc.
Ok, let's move on from the analogy and compare two grossly over-exposed images made in my D800 as a result of classic brain fade. One is a raw file and the other, a JPEG - as they came out of the camera:
Unprocessed RAW file
Unprocessed JPEG file
It's probably fair to say that the JPEG is a little better than the raw file, but neither is useable. But what if we run these two files through our "electronic darkroom", which in this case is Capture One 9:
Processed RAW file
Processed JPEG file
I think you'd agree that the processed raw file leaves the processed JPEG for dead.
So why is this? Put simply (very simply in fact), a raw file is an unprocessed record of the light falling on your sensor. It carries information about what your camera thought the exposure and colour balance should be, but because all the data are still there, you can adjust as far as the file will allow. A JPEG on the other hand is produced when your camera looks at the raw data, decides things like exposure and colour balance - and then writes what's needed to the file - and disposes of the rest. That's why formats like JPEG (and GIF) are called "lossy". And that's why raw files are big (in this case, 35 meg) and JPEGs are relatively small (2 meg): the raw file still has all the original information. (There are other differences like bit depth, but we needn't worry about that.)
JPEGs have their place. You wouldn't want to send a photo of your kid's party to your family in raw format. What's more, some cameras (like Fuji for example) do a brilliant job of producing JPEG images. But if you make a mess of your exposure as I did, or you are shooting difficult subjects such as sunsets (high contrast) or in low light, you want all the data your camera can give you to make adjustments.
So, if you haven't tried raw, give it a go. Many cameras can shoot both raw and JPEG simultaneously and if yours can, there's really no risk in giving it a try.
You'll just have to be prepared to delve into the new (and creative) world of the digital darkroom!