BARF stands for bones and raw food and is just that - a diet comprised of raw meat and bones such as mince, chicken wings, lamb ribs, pork ribs, rabbit plus pulped vegetables, raw eggs etc.
As to whether or not it may benefit your dog that's something really only you can decide, if you want to do some research there are a few books available, Dr Ian Billinghurst has written a couple which are available on Amazon. I had Alfie on a BARF diet but have recently taken him off it again for various reasons. He still gets raw stuff a few times a week but it's no longer the basis of his diet.
Some dogs are naturally just leaner than others, Alfie being a case in point, he is a real skinnymalink but that's just his natural state and he is very healthy.