Eleazar is one of the Denali coven, the mate of Carmen. He used to be a member of the Volturi
debate team guard, using his gift for identifying the gifts of other vampires to ensure that Aro didn't miss out on any super special sparklepires that he might want to keep. When he met Carmen, he left the Volturi and the two of them went off on their own, and eventually joined up with Tanya & co. The fact that Aro - who had killed Didyme to make Marcus stay - let this happen is evidence that he's an idiot odd, given that Eleazar's powers are considerably more useful than Marcus'.