About Proofs
The word "proofs" can mean different things to different people, so be sure to talk to your photographer about exactly what it means in your case.
Generally speaking a proof is an unretouched photo that is not 100% ready for printing as-is. It's just an image that will give you an idea of what your final print will be of. This type of unretouched, quickly developed proof is especially common with film photography, since it's a lot more work to do even basic retouching or editing with a photo created via film.
With digital, sometimes a proof will have some editing done on it, or sometimes it may even have had major editing and retouching done on it.
In both cases they may also be stamped "proof" or have a watermark across the image (usually the photographer's name or company name). Usually the final photo will look better than the proof, since it will have been printed with care and retouched where necessary.
Your proofs may be thumbnail sized, or they may be 4x6, or they may be somewhere in between and bound with several photos on a page in a proof book. They may be printed, they may be viewed online only, or they may be available both as prints and online.
Regardless of how the proofs are presented, the main purpose of them is for you to be able to pick the photos you or others would like printed.