For me the answer to the question, “why does my cat lick me?” comes from personal observation. My cat looks upon me as a mother cat. All domestic cats do the same. Our cats are kept in a state of perpetual kittenhood with us as we provide for them and unwittingly dominate them by our sheer presence. Kittens are licked by their true (cat) mothers during the early days. When I stroke my cat she thinks I am licking her as her mother did. It feels that way and is a very similar action.
Photo by tilaneseven – this is a Flickr photographer
In return my cat will lick my hand sometimes. It is a friendly return gesture in recognition of my friendly gesture. I might not be stroking her, in fact. It might be a human form of friendship that she has picked up as being equivalent to her mother’s lick. For example, I might talk to her quietly and cuddle her. There are a whole range of intimate and friendly gestures that might provoke her to lick me and it is not always on the hand. She sometimes licks my face as is the case for the person in the photograph.
There might be other reasons as to why my cat licks me. It might be the taste of my skin (maybe there is something on my hand or my skin might be salty through sweating) but this is relatively rare for me compared to the friendly exchange of linking.
Sometimes my cat will do a lick/bite. The lick extends to a very gentle nibble on the hand or even my face if it is near her face. You can see a mother’s lick going to a gentle bite (loving bite) in this video of F1 Savannah Cat MAGIC. It is about 2/3rds of the way into the video.