Coriakin is a former Star who was sent to govern the Island of the Duffers as a sort of punishment for some offense committed. He is a magician and governs the Duffers with a firm but kind hand, yet is treated with suspicion and distrust despite treating them well. He permits the Duffers to turn themselves invisible, but it turns him invisible as well, and due to his sudden disappearance, the Duffers fear him more than ever.
When Lucy arrives to remove the spell, she too is afraid of him, until the spell is broken and Aslan introduces her to Coriakin, who in reality is very kind and treats Lucy to a wonderful lunch. Besides Aslan, he's the only Narnian to know about the existence of Earth.
Coriakin puts his magic to good use by creating a magical map for Caspian showing him the places he'd been and some of the places he'd go, and by repairing the Dawn Treader and filling her up with supplies and useful gifts.
How long he remained on the Duffer's Island, and whether he was ever to tread the skies as a Star once more, is not known.