Most digital cameras process and compress the pictures you take immediately after capturing the image. This can be helpful, as it keeps the file sizes low (using JPEG compression) and takes care of color correction, including white-balance, tint, and exposure, so you don't have to. However, some people, such as professional photographers, prefer to have more control over how each image is processed. Therefore, many high-end cameras have the ability to shoot in RAW mode. This mode does not compress the images at all and leaves them completely unprocessed.
Because Camera RAW files are uncompressed, they take up more space than typical JPEG images. In fact, RAW files often require 2 to 3 times more space for each image captured. So, you'll want to have an extra-large memory card in your camera if you plan on shooting in RAW mode. But since RAW photos are not compressed, you maintain the full quality of each image. This can make a noticeable difference when printing images, especially for large prints.
Camera RAW files are also unprocessed, meaning all the photo processing is done on the computer. It is like taking a film negative to a dark room to be developed. The RAW file is the negative and the computer serves as the dark room. With a RAW file, you have complete control over the temperature adjustments (for white-balance), tint, hue, and exposure. However, since Camera RAW files are not typical images, most image-viewing programs will not open them. Therefore, most camera companies include Camera RAW editing software with their high-end cameras. These programs allow you to open RAW files, do the necessary processing, and save them in common image formats such as bitmap, TIFF, and JPEG.
While shooting in Camera RAW mode offers a lot of control over your photos, it takes additional software and extra time to open and edit each picture you take. For most casual photography, using the camera's built-in processing is the most suitable option.