Cepheus is the King of Ethiopia and the father of Andromeda. He decides to sacrifice his daughter to the sea monster in order to save his kingdom from the wrath of Poseidon. However, he agrees to let Perseus marry his daughter in return for the hero slaying the monster. Like many of the other characters in the story, Cepheus has a constellation named for him today.
For more on Cepheus, see "Themes: Sacrifice."