The Covenant believe that when the Halos are activated the Covenant will embark on a "Great Journey" similar to that undertaken by their gods, the Forerunners. Finding and activating the Halos is a prime goal of the Covenant.
However, a few of the Covenant are aware that the Halos, when activated, destroy all sentient life in the galaxy. 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 propel them into the "Divine Beyond", a heavenly paradise they will share with the Forerunners.
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.
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. Following this, he helped some UNSC troops stop Tartarus from activating Installation 05, and hence the entire remaining Halo network. The loyalists still seem to believe in the Great Journey, and will most likely continue to try to activate the Halos.
See Also
Trivia
In the Lord of the Rings world the Great Journey, or the Great March was the journey that the Elves known as the Eldar took from Cuiviénen, the place of their awakening, to Valinor.