Cats naturally have an instinct to sharpen and renew their claws; as well as release their own scent (which can be done by scratching because their front paws contain scent glands). This is why you will see cats scratch, including indoor cats. One way to stop indoor cats from scratching up your floor and furniture is to invest in a scratching post. These can be purchased at any pet store and nearly any department or grocery store that carries pet supplies.
Scratching posts can be introduced to a cat at any age but the younger the cat, and the earlier you teach it to use the scratching post, the more likely they will adapt to using that instead of your furniture. Try placing catnip on the scratching post to entice the cat to use it.
You can also deter a cat from using furniture, or other objects, as scratching posts by using a water bottle with a spray nozzle attached to it. When you see the cat attempting to scratch (or perhaps already is), spray it with a quick shot of water. As cats generally do not like to get wet, they will learn quickly that they do not want to continue the behavior.
Most people do not have a problem allowing the cat to see who is spraying them (a sort of authority measure), but some believe that you should stay out of sight when using this form of behavior management in order to reduce the possibility of the cat losing trust in the person spraying them.