The radical religious group known as the Covenant worship a civilisation that lived long before humans called the Forerunners. It is the belief of the Covenant that the Forerunners were gods who used the Halos or "Sacred Rings" as they often refer to them, to transcend to a "Great Beyond". They believe that they are the rightful inheritors of the Forerunners' legacy and that it is their destiny to activate the Halo arrays and transcend to the same higher plane of existence.
In reality the Forerunners were not Gods, and created the Halo arrays to destroy all life in the galaxy as a way to deprive the parasitic and highly dangerous lifeforms known as the Flood of a source of food and wipe them out. The Forerunners disappeared from the universe when they were forced to activate the Halo rings and cause their own extinction.
Halo: Combat Evolved, 2, and 3: ODST
After the United Nations Space Command accidentally discover one of the Halo rings near the beginning of Halo: Combat Evolved, and discover more rings throughout the games, a violent struggle breaks out between the UNSC and the Covenant for control of them. In Halo 2 and Halo 3: ODST the Covenant unleash a fleet on Earth to and around the city of New Mombasa in Africa in an attempt to acquire a piece of technology that will open a portal to Installation 00, or "The Ark", a Forerunner world from which all Halo arrays can be activated, and that the Covenant believe will start the Great Journey.
Near the end of Halo 2 the Elites, the species in command of the Covenant fleets, are stripped of their power, with their position being handed over to the species known as the Brutes. During the resulting unrest they learn that the Great Journey is a myth, and the Covenant divides into the factions of the Loyalists, who continue to try and work towards the Great Journey, and the Separatists who ally with the UNSC to stop them.
In Halo 3, despite the best efforts of the UNSC, the Covenant Loyalists are able to excavate the Forerunner technology and create a portal to the Ark, where a fight breaks out between the UNSC and Separatists, and the Loyalists. Knowing that the Covenant cannot activate the Installation themselves, the Covenant leader, the Prophet of Truth, kidnaps UNSC Sergeant Avery Johnson to act in his place. This is necessary due to the fact that the Covenant are not the rightful inheritors of the Forerunner legacy, but instead Humanity are.
The Prophet is stopped and killed by a combination of the UNSC's Master Chief, the Covenant Seperatists' Arbiter, and the Flood Gravemind. After this failure to achieve the Great Journey, and the UNSC activating the rings to again achieve their true purpose and destroy the Flood, the Covenant effectively disbands.