Are you able to get a good look at your cat's claws? If there's any redness of the skin around the claw, or discoloration of the claw bed (extend the claw), or your cat acts like he's in pain while walking, then your cat may have a medical problem and need to be looked at by your vet. (here's a brief overiew of the potential problems, but your cat needs to be seen by a vet for treatment).
If there's no problems, then don't worry, it's normal, especially if your cat doesn't have access to a scratching post (or the post is defective in some way, not big enough, wrong material, wrong shape (horizontal or vertical scratching surfaces are preferences).
When cats claws grow, they get longer AND grow layers. The outer layers need to be stripped off. Normally, this is done by clawing something, but if the scratching surfaces are inadequate, she'll try to scrape if off with her teeth.
I've manually removed the outer layers occassionally when trimming claws, but I think it hurts them so I stopped doing it.