Before considering what RAW is let’s first understand what a JPEG is. A camera (any camera, from your phone to a pro level DSLR) will first capture the basic elements – i.e. the colour of every single pixel which collectively make up your image. It will then process that information and create the finished article (JPEG) that it thinks you want. This may be influenced by the settings you selected when taking the shot – for example you may of selected black and white – the camera will of taken the image in full colour; the camera’s software will of then changed it to black and white.
RAW mode does not perform that processing, and allows you to do the work of the camera’s software manually on a computer.
If you are familiar with film photography think of RAW as the negative that you took to the lab for processing to create a print. The RAW image is your digital negative, and you and your computer are the lab.
Whilst RAW mode allows you to make significant adjustments to your images it is not a substitute for taking a properly exposed, focused and composed image. A great image always starts at the beginning. Great chefs will only use the finest ingredients to create their masterpieces; a quality RAW file is the beginning of that finished image you have in your mind. Shots taken as JPEG are the ready meals of photography.
Why use RAW mode?
Fireworks are perhaps the perfect example of why you should use RAW. The dynamic range from the dark shadows, to the intensity of the explosions is a challenge for even the most expensive camera to get right. The first image below is the RAW as it came out of the camera, the second image is after processing.
As shot 
Processed
RAW mode gives you total control of the creative process – but perhaps the biggest advantage of RAW images is in the future. Look at that black and white shot in 10 years time that you loved so much when you took it and you may wish it was colour after all – with RAW mode you can start over and re-process as you wish.
See my article on how to photograph fireworks if that’s of interest.
The only disadvantages of RAW mode is that they are very large – my Canon 70D produces RAW files around 4 times the size of JPEG – and you have to process each image before you can do anything useful with it such as print it, share it on social media or display on a website, so it’s not for every occasion. For example if you take your camera to a party and your aim is to capture the moment instead of taking masterpieces then of course JPEG is the way to go – you won’t want to be processing the 200 images you took before you can use them.
My camera is permanently set to shoot in JPEG and RAW – i.e. each shot is stored as a RAW file and a processed JPEG so I have the best of both worlds, and I don’t run the risk of making the mistake of spending hours on a landscape photo shoot to get home and discover I have been shooting in JPEG.