Vet at FirstVet answers:
Cats lick and groom each other (and people) to show that they belong in the same social group.
Cats that excessively lick their owners have often been taken from their mother too early and developed a dependent relationship with their owners.
If a cat licks you consistently, without stopping, there is often some kind of underlying problem. It is wise to consult a veterinarian or an expert in cat behaviour. If the licking bothers you, try to interrupt the behaviour by getting up and walking away.