A proof is a preview. Proofs are used to select which images will get further work and/or be included in a project, or will be bought by the customer.
Some photographers make prints for proofing, some use a computer display or projector to show proofs.
There is also soft proofing, which is displaying on a computer display an close approximation of what a print will look like.
Computer displays are back lit and use the RGB color model to display colors. Prints are fore lit and are made using the CMYK color model, making a print look different from a computer display.