Why are cats so fastidious?
Cats' love of cleanliness is a major reason why people want to keep them as pets. In fact, a cat's grooming is entirely a physiological need. This is easy to understand by simply observing when a cat likes to groom itself.
Cats typically groom themselves after eating and playing, after vigorous exercise such as chasing prey, or after waking up from a nap in the sun. During hot weather or after strenuous exercise, their bodies generate a lot of heat, which they must expel to maintain a constant body temperature. 
Cats use their tongues to fluff their fur, promote heat dissipation, stimulate the secretion of sebaceous glands, make their fur shiny and smooth, prevent it from getting wet easily, and allow them to ingest small amounts of vitamin D, which promotes normal bone development.
Cats spend time grooming themselves every day. Their rough tongues remove loose hair while licking their fur, but if the hair is swallowed, it can clump together in the stomach and form hairballs. Hairballs can significantly affect a cat's health, so as an owner, you should regularly help your cat "clean" their fur to prevent hairballs.