The obvious reason why domestic cats lick their owners is because it is a sign of affection but there may be alternative reasons, which I discuss here. I say this because scientists have not yet investigated this form of feline behaviour, which surprises me.
The commonsense reason is the one stated in the first line. It looks like that. In fact, it looks obvious to me that this behavior is designed to tell their owners that they like them and are thankful for what their owners provide which is security, food and companionship.
This theory is supported by the fact that when two cats don’t like each other they never groom each other (allogroom) except if one wants to make friends. And let’s remind ourselves that it is highly likely that our cats relate to us and interact with us as other cats.
However, there may be some alternative reasons and incidentally if a cat does not lick his owner it may be because the owner has actively shunned it. This might be because the cat’s tongue is quite harsh (with backward facing keratin spines) designed as it is for self-grooming of fur. To some people it can feel uncomfortable if their cat licks them for a long time.
One alternative reason as to why cats lick their owners is because they like the taste of their owner’s skin which is salty. That’s a fairly common assessment but cats don’t, as far as we know, have a strong preference for salty flavours.
The reason is much more likely to do with our cat’s relationship with us. Dr John Bradshaw believes that sometimes cats lick their owners to attempt to apologise for something that they think they have done wrong. He suggests that this may be something that we have not even noticed.
A further alternative might be that if a cat licks his owner’s hand with one paw placed over her wrist this may be an attempt to exert control over his owner. I have never got the impression that this is likely. If a cat places his paw over a person’s finger or hand and then licks the finger, to me, it indicates that the cat wants to keep the finger still so that he/she can do a proper job. That may be anthropomorphising cats but I think it is a practical answer.
I would have thought, in conclusion, that 95% of the time when cats lick their owners they are conveying to their owner a sign of affection and it is an act designed to increase the bond between cat and human. It is exactly what we see between cats themselves.
P.S. This is something I omitted to say. Cat show their affection towards us in other ways such as rubbing up against us, head-butting us, and snuggling up against us. Licking us is just one more manifestation of their affection towards us.