High Prophets
From Halopedia, the Halo wiki
The three High Prophets serve as the highest leaders of The Covenant High Council, being theocratic and known as "Hierarchs". The Hierarchs are thin, hunched creatures with large craniums that float on levitating Gravity Thrones decorated with golden backs, equipped with energy shielding, and armed with Gravity Cannons; they wear crowns adorned with small holographic projections of Halo; they have the ability to access teleportation grids.
Prophet of Truth
Little is known about Truth, except that he is the remaining Hierarch at the end of Halo 2 who offered the former Commander of Alpha Halo to become the Arbiter and ordered him to defeat the Heretics, rebels that regarded Covenant teachings as false, and to retrieve the Sacred Icon on Delta Halo.
He spearheaded the purge of the Sangheili councilors for their opposition to the Brutes, becoming the new Honor Guards of the Prophets, sparking the Civil War.
When Gravemind teleported Master Chief to High Charity, Truth betrayed Mercy ,who was wounded by a Flood Infection Form, and escaped to his Forerunner flagship, but not before Master Chief follows him.
Truth then led the Covenant Armada to Earth. Once there, he landed the Forerunner Ship on the Cartographer Facility, which activated and opened a portal to the Ark. Once onboard the Ark, Truth took up residence in the Installation's Control Room.
Soon after, the Humans and Elites followed through the portal to the Ark. They took down the defenses surrounding the Control room. High Charity then appeared through the portal. The Master Chief and Arbiter then proceded into the Control Room. The Arbiter then cut down Truth with his sword, putting an end to the deceitful Prophet.
Prophet of Mercy
Oldest of the three High Prophets, Mercy was first seen present at the trial of the Supreme Commander of the Fleet of Particular Justice, but decides to try something different than an execution for the shamed Sangheili. Mercy agrees with Truth in promoting him to Arbiter, and then sending him on a mission to kill "the real Heretic". Upon completion of his mission, he plans to invade Earth a second time (after Regret's botched invasion, this time perhaps to secure the Ark, begin the Great Journey, and wipe out the Humans). Before he can succeed, he is attacked by the Flood on High Charity and infected. Seeing this, Truth tells Tartarus to "let him be" and then tells Mercy, "The Great Journey waits for no one, brother. Not even you." Mercy tells Master Chief where Truth is going and dies.
Prophet of Regret
Regret is the youngest of the High Prophets. Contrary to his name, he appears to be reckless and headstrong.
Regret led the initial, botched attack on Earth. He landed troops in New Mombasa, East African Protectorate, the only place the Covenant landed on Earth. The invasion is foiled, due in part to the actions of Master Chief, and he then fled to Delta Halo. It is speculated that he was not at all aware of the importance of Earth to humanity and simply assumed it was another world that had at one point been inhabited by the Forerunner. This accounts for his fleet being far smaller and much less prepared than the fleet that destroyed Reach. His actions did not win him a reprieve. Master Chief pursued and eventually assassinated him.
The quality of being dead does not entirely hinder the Prophet of Regret, as he makes a final appearance later in the game (revived to a degree by the apparent Flood leader Gravemind) in which he argues with 2401 Penitent Tangent.
Past High Prophets
The High Prophets are usually replaced all at the same time through political machinations. Previous High Prophets include the High Prophet of Restraint, the High Prophet of Tolerance, and the High Prophetess of Obligation. These three hierarchs were deposed of when Truth, Mercy, and Regret came to power.