Kadaj is a young man who leads a group of three people who plan to bring back Sephiroth by using the Jenova head they find at some point during the story. The others in the group are called Loz and Yazoo and like Kadaj, are excellent fighters. Kadaj uses a twin-bladed sword as a weapon and will fight with Cloud before using the Jenova head to bring Sephiroth back.
Kadaj and his gang are the reason Cloud is forced to fight once again. They summon a Bahamut creature to cause chaos in the town of Edge, which means Cloud and his friends have to stop it.