JPG (JPEG)
JPG is a lossy form of compression. If you’re shooting in JPG, your camera takes each image and discards some of the information it doesn’t think you need. Why? To make the file size smaller. Which means you can fit more images on your memory card and your computer.
You can also control the amount of compression in your camera’s settings. The more it’s compressed, the lower quality your image is going to be and the file size will be smaller. If you decide to shoot in JPG, edit copies of your original file, not the original.
RAW
RAW doesn’t compress your images. If you’re shooting in RAW, your camera takes each image and saves every little bit of information it can, even things you probably can’t see with your eyes. Your files are going to be much larger and will take up more room on your memory card and your computer. But you’ll have more information and more control over the editing process.
PSD
PSD doesn’t compress images. To preserve all Photoshop features (layers, effects, masks, and so on), save a copy of your image in Photoshop format (PSD). PSD documents support files up to 2 GB in size.
Note: I usually work in my PSD files and save out a flattened TIFF to place in other applications or send to printers/designers. I will convert my TIFF files to CMYK (if needed) and leave the PSD in RGB. Some people prefer to work in a layered TIFF, and that seems to be fine too.