The spiritual and political leaders of the Covenant are the Prophets, with their hovering chairs and their elaborate headdresses. They are guarded by Elites and, although not as physically imposing as them, are supposed to possess deadly and "unique" attacks.
At one point Bungie mentioned the possibility of being able to distinguish individual Prophets from one another by their headdresses.
Prophets may have specialized, individual roles in Covenant society. At least two specific prophets have been mentioned in various places: the Prophet of Truth and the Prophet of Regret.
The Halo 2 manual says their significance is "administrative or religious in nature" and notes they have never been seen on a battlefield, and never captured or killed.