The Siren has the ability to resurrect enemies that Booker has already defeated in battle. If you can manage to defeat her then all resurrected enemies will die also.
EGM’s TAKE: The Siren adds an extra thought process in combat, she may not deal as much damage as other heavy hitters, but you can quickly become overwhelmed by the enemies that she resurrects. You are forced into making a decision, whether to go directly after her or destroy the enemies that are physically hurting you first. Spend too long deciding and you will find yourself in a lot of trouble.