From Halopedia, the Halo wiki
A Luminary is a Forerunner device designed to scan for and identify Forerunner relics. The Covenant reverse-engineered their own Luminaries, modeled and sculpted after an original Forerunner device recovered from the Covenant-controlled Forerunner Dreadnought. The Luminary is an essential piece of equipment on all Covenant vessels.
A standard Covenant Luminary is shaped like a series of three silver pyramids: two smaller ones supporting an upside down larger one in the center. There are apparently several models of Luminaries, more advanced versions (presumably a better reconstruction of the original Forerunner devices), as it was noted that primitive versions of Luminaries led the Covenant to discover the Lekgolo, shortly after the formation of the Covenant.
Luminaries are of great religious significance to the Covenant and tampering with them was punishable by death. A Holy Writ, essentially the Covenant equivalent of folk wisdom, concerns the Luminaries, namely, "A Luminary does not lie." A writ (either the Writ of Sanctity or the Writ of Security) also ordered the destruction of any luminaries onboard a ship that was compromised in battle, so that they would not fall into enemy hands.
As the presence of a Luminary is required on all Covenant vessels, there are likely at least tens if not hundreds of thousands of them in existence, depending of course on the number of ships the Covenant control. The Luminary of the Minor Transgression is significant as it led the Covenant to the UNSC colony Harvest, and precipitated the Human-Covenant War. It identified Harvest with several thousand Forerunner glyphs (referred to as Luminations in this context and called relics by the Covenant) that led the Covenant to believe the world held innumerable Forerunner treasures. Unfortunately, they misinterpreted the sign as "Reclamation," rather than the actual translation, "Reclaimers."
Although the newly appointed Prophet of Truth was made aware of this mistake by Mendicant Bias, he refused to let the Covenant know of humanity's relationship to the Forerunners (or, rather, his assumption that the Reclaimers were actual descendants of the Forerunners) as such a revelation directly contradicted the basis of the Covenant faith: that every Forerunner transcended to godhood, and so would anyone who followed in their footsteps. Instead, he claimed that Humans destroyed the relics at Harvest, and would do the same to the Halo rings should they ever find them. He also planned to use the Luminations as a means of tracking down the survivors of Harvest and wiping them out. 
On very rare occasions, the Covenant would also find original Forerunner Luminaries pointing to specific artifacts of high importance. For example, Mken 'Scre'ah'ben's expedition party discovered a Forerunner Luminary pointing to the Halo rings' locations on Janjur Qom, only for the device to be lost before the expedition could return to High Charity. In 2551, Covenant forces under the Prophet of Regret's command discovered a Luminary on Meridian pointing to Installation 00 and the Portal on a planet known as Erde-Tyrene. Seeking to outdo his fellow Hierarchs by claiming the monumental discovery for himself, the Prophet of Regret took the Fleet of Sacred Consecration to the Portal's location, unaware that Erde-Tyrene was actually humanity's homeworld, Earth.
The UNSC developed the VECTOR-class Mjolnir armor based on Covenant technology, for Spartan-IVs to commune with Luminaries. This was notably used to seek artifacts among the debris of Alpha Halo on Basis.
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