Covenant religion
From Halopedia, the Halo wiki
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The Great Journey is a central theme for the Covenant and its theocratic government; it is their ultimate goal. It is also that which stopped the war between the Prophets and the Elites. The Covenant believe that their ancestors, the Forerunners, used the Sacred Rings to cleanse the universe of all that is unholy, escaping a doomed existence of fighting an endless struggle against the Flood, and allowing them to transcend into gods, giving them ancient and unlimited power. The Covenant wish to activate the Halo installations to wipe out humanity and the Flood, which would provide salvation for their doomed existence and allow them to follow the Forerunners to their mysterious destination, where they will share in their power. In Covenant Religious terms the Flood are known as one of the many "obstacles" or "tests" that the covenant must pass to begin the Great Journey.
The Heretic Rebellion
A few of the Covenant, called Heretics, were aware that the Halos, that when activated, would destroy all sentient life in the galaxy that included themselves. The Heretics are led by the Elite Sesa 'Refumee, who discovered the true purpose of the Halos from 343 Guilty Spark , the Forerunner construct. Refumee was killed by The Arbiter on the Threshold Gas Mine, and the heresy destroyed.
The Covenant's beliefs
Whether the High Prophets do know the true effects of activating a Halo is uncertain, but the very fabric of the Covenant is built on accomplishing it, believing this will be akin to following in the footsteps of the Forerunners and propel them into the "Divine Beyond", a heavenly paradise they will share with the Forerunners.
The Jackals are not thought to believe in the Great Journey. They are simply mercenaries hired by the Covenant to be scouts and snipers. Because they have been a part of the Covenant for a very long time though, it may be that in time they came to believe in the religion of the Covenant.
The Engineers are unknown but they seem to be very religious toward the covenant, The Great Journey. Some also seem to not care much. It is currently unknown where they lie.
The Elites once had faith in the Great journey, but eventually discovered the truth and rebelled, joining the UNSC.
The currently living Arbiter, who is either leading or an important member of the separatist movement, knows the true function of the Halos after speaking with 343 Guilty Spark, a Monitor of the lost Installation 04 who is considered by the leading Covenant caste as one of the holy oracles. Following this conversation he, with the help of some UNSC troops, attempted to stop Tartarus from activating Installation 05, and hence the entire remaining Halo network, but failed. In the final cutscene(s) of Halo 2 the network is described to be in a standby status, pending activation from The Ark. The loyalists still seem to believe in the Great Journey, and will most likely continue to try to activate the Halos.
The UNSC
As the Master Chief and UNSC discovered, the Halos were not built as religious icons; they are galactic weapons of mass sterilization built by the Forerunners to contain a parasitic race known as The Flood. After exhausting all other options to destroy the flood, the Forerunners activated the rings, allowing all sentient life to die, eventually starving and killing the Flood.
Activation
The Prophet of Truth traveled to Earth to begin the Great Journey by activating the massive structure buried beneath New Mombasa which was once thought to be the ark. Apparently, the sole purpose of this unearthed construct , is to generate a portal which leads to the true Ark, Installation 00, which lies 2^18 light years outside the milky way galaxy.
On The Ark, during the Halo 3 campaign, several terminals can be found left by the Forerunners, describing the activation of the Halo arrays as the Great Journey. Through such terminals on other Forerunner installations the Covenant may have learned of the Great Journey, and used that name.
The Prophet of Truth attempted to start the Great journey in The Covenant (Level, but was stopped by the Artbiter who killed him.