Cats are diligent in grooming themselves, but some cats also actively groom their owner's hair. A "beautician cat" might perch on the back of a chair or above your head in bed and comb through your hair with its teeth and paws. Sometimes the cat will even hold your head steady or object if you move out of reach.
Cats' grooming behavior can be a physical and social issue. Their physical and emotional health, as well as traits of instinct, influence how a cat acts and reacts. Think of this as the H.I.S.S. Test, which stands for health, instinct, stress, and symptom solvers.
Health
Grooming keeps skin and fur healthy and clean. Cats spend a good portion of their awake time in some form of grooming behavior.
Instinct
Kittens begin to groom themselves as youngsters. Much of the grooming behavior is instinctive, but it's also influenced by the environment. If Mom is a neatnik, then chances are the babies will also grow up with clean "cattitudes." But slovenly Mom-cats may pass on their grooming indifference to offspring. Mom-cats also groom their babies to keep them clean, and social cats groom each other and share communal scent.
Stress
Cats also use grooming to relieve stress. You could compare self-grooming for stress relief to a human getting a relaxing massage. Other times, cats can use "power grooming" as a way to intimidate other felines and chase them away from a favorite territory.
Symptoms, Signs, and Solutions
If your cat is grooming your hair, it is likely to be using grooming as social behavior. Cats groom other cats in their family group when they like each other and have friendly relationships. The licking also spreads scent, so the cats that sleep together and groom each other smell alike. This creates a sort of "family perfume" that identifies each other as safe and friendly. If the cat suddenly starts out of the blue, maybe she likes the smell of your new shampoo.
When your cats groom you, they aren't interested in creating proper feline hairdos (well, maybe some cats have a style in mind). More likely, cats that target an owner's hair simply trigger on the "furry part" of the human and want to share the family scent with proper grooming.
The cat might receive some sort of reinforcement that encourages them to repeat the behavior. Do you talk to the cat and pet it during this grooming? Or it may be enough simply to respond if your cat taps your head to get you to move back into range if you move away.
The behavior can become a bit aggravating when overdone. Some cats pull out the owner's hair or chew it off, just like they can over-groom themselves from stress. The pulling/chewing behavior may be an extension of the wool-sucking sorts of targeting Oriental heritage cats often seem to indulge. That behavior may stem from a nutritional deficit in some cases. The potential for hairballs exists if your cat swallows long strands of human hair. If a cat seems to want to eat your hair, it's a good reason to go to the veterinarian for a check-up.
You can offer kitty a substitute such as a fuzzy stuffed toy, and shoo the cat away from your head to prevent being snatched bald. But in most cases, consider a cat grooming a human's hair to be a huge compliment and gesture of affection, sort of the kitty equivalent of a petting session. Don't worry, the cat won't expect you to become kitty beauticians with a lick and a promise. Petting will do.