Shed bits of body;-- fur, claw sheaths (kind of like fingernail clippings for a person) blood, or tiny amounts of urine or poop are what is called "spoor". Cats are one of the animals with a strong instinct not to leave spoor around. This is because the spoor carries the cat's scent.
In the wild, many other animals will eat cats if they can catch them. Animals that hunt using smell (like bloodhounds) could follow a trail of spoor to the cat or a nest of kittens if a cat left spoor around. Cats have an instinct to get rid of spoor in several ways. You have seen your cat cover up it's poop etc... when it uses the litter box. It is burying its spoor. When it's something like little fluffs of fur spread all over a carpet, the cat will try and lick them up.