Cats use their claws to help them keep their footing on slippery or smooth surfaces -- or when they're fighting or sharpening their claws. Cats can use the claws on their front paws to hold onto things, as well. The front claws are more versatile, though not as strong as the claws on the rear feet. To protect his claws from damage, a cat will withdraw them into their sheaths.
Your cat needs a place where she can scratch her claws and wear off the layers of dead skin that cover them. A scratching post or board is best for this purpose. Especially for housebound cats, a scratching post is a must.
To help keep your cat's claws healthy, examine your cat's paws regularly (roughly once a month) to see if the claws need clipping. You can get the veterinarian to cut them the first time and to show you how to do it, and then take over yourself once you feel confident about doing it properly. Use ordinary nail clippers or special ones from a pet shop. Work in a good light so you can see -- and avoid -- the pink dermis or "quick" growing at the base of the claw. Cut the nail in front of the quick -- if you cut through it, it will hurt your cat, and the cut will bleed a lot. The bleeding will eventually stop, but your cat will be much less likely to cooperate in future claw-clipping exercises!
Though many people opt to de-claw their cats, de-clawing is not as good an idea as it may sound. The vet must actually amputate a small piece of the cat's toes to remove the claws, which means surgery under anesthesia, always a risk for cats. A de-clawed cat cannot defend itself if it goes outside, and can experience chronic paw pain, difficulty moving around and difficulty using the litter box.
If your cat scratches inappropriately, try offering a scratching post, or use some simple, kind behavior training to get him to stop. Read Good Habits for Cat Owners for tips on how to stop problem scratching.