Creon is the king of Corinth, who welcomes Jason into his city when the hero is forced to flee from Iolcus. Later on, Creon signs off on Jason marrying his daughter, Glauce. This causes Jason's other wife, Medea, to go nuts and kill Creon, Glauce, and her and Jason's kids. So, Creon's attempt to make his family look cool by having a hero as an heir goes totally wrong and ends up destroying them all.
Note: Sometimes this Creon is confused with the Creon of the Oedipus plays, but they aren't the same guy. (Way to make things confusing, ancient Greece.)
For more on this Creon's awful death, check out Shmoop's coverage of Medeaby Euripides.