Many people assume that cats lick them as a sign of love which isn't really that far off. While it's hard to determine if cats feel complex emotions like love, licking is a sign of affection. Cats usually lick themselves in order to groom. Mother cats will lick their kittens as a part of the grooming process as well. However, cats will also lick each other as a sign of affection. Cats actually lick humans for one of several reasons, but most of them come down to displays of affection.
Signs of Affection
In the same way that you show affection to your cat by petting it, your cat may attempt to return the favor by licking you. Kittens especially will use licking as a way to ease anxiety the way a human might use hugs. If your feline friend loves to lick you, it probably means it would like some affection in return. Which, honestly, is one of the best parts of owning a cat.
Cats use pheromones to mark their territory. While most people know that cats mark property by urinating on things, they can mark their territory in other ways as well. Licking and head rubs are ways for cats to claim you as part of their property—affectionately. When your cat licks or rubs against you, it is reaffirming that you are important to it and they want all the other cats to know. You may notice that sometimes other cats shy away from you, it's possible they smell that you belong to another cat.
Part of the Family
Many people joke that cats think they're humans and given the way some cats behave towards their owners, it's easy to see why. A great example is a cat who will leave dead mice or birds on their owner's doorsteps in an attempt to share a tasty treat. Cats have also been known to present their owners with live animals in an attempt to teach its owner to hunt. It's clear that not only do many cats see their owners as part of the family, they also see them as a bit inept at being cats. Female cats especially will exhibit this sort of parenting or nurturing type of behavior.
When cats lick you, it can mean that they are attempting to teach you to groom yourself. It's a memory your cat had from being licked by its own mother and is a real sign of affection. Cats will also lick each other as a way to calm them down. Cats are very attentive to their owner's moods so you might find your cat is more affectionate when you're stressed or sick. Cats are attempting to calm your anxiety the same way you would pet your cat if they seemed nervous.
But It Hurts
A thorough cat licking isn't always the most comfortable experience. This is because cat tongues have backward-facing hooks that are meant to pull and clean their fur the way a comb would. Remember, to your cat being licked feels good, it doesn't know it is hurting you. When a cat licks you it's just trying to show some love.