Aeons are not like summons in previous games. You call them into battle, and they stay there instead of doing a single attack, and they are just like a controllable character, with selectable attacks, HP and MP and an overdrive gauge. When you summon it, it replaces the three characters currently fighting, and you can only summon one Aeon at a time. When it dies, it isn't game over - the three characters return to continue the fight.