The reasons why cats keep licking their owners’ arms are as follows:

Leaving a scent. Cats have a keen sense of smell and like to leave their scent on their bodies to mark their territory.

Clean. Cats have very sharp tongues and they like to lick their fur and skin to keep them clean. At the same time, cats will also help their owners clean dirt or dust from their skin through licking.

Coquettishly. A cat licking its owner's arm may also be coquettishly asking the owner to pet it.