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Triluminols are compounds preferred in the development of Display Technology. The triluminol is a triangular shaped Minbari crystal with a small chip in the center. The full extent of its abilities are unknown, although it is said to be the holiest of all relics in Minbari society and thus any readings it gives are beyond question. The primary use seems to be the ability to detect people who contain the DNA of the Minbari prophet Valen. Valen was really Commander Jeffrey Sinclair after he traveled back in time with Babylon 4 to help the Minbari defeat the Shadows in the previous Shadow War. In one instance Minbari ambassador Delenn used the triluminary as part of a device which transformed her into a Human-Minbari hybrid. In another, 3 of them are used to change Jeffrey Sinclair into a similar hybrid.
Also, in the final moments of the Earth-Minbari War, the Grey Council used a Triluminary as they attempted to interrogate Sinclair, whom they had captured. The Triluminol glowed brightly, indicating that Sinclair had Valen's DNA so the Council assumed that Sinclair had Valen's soul and was the reincarnation of Valen himself (not knowing that Sinclair was in fact Valen himself, prior to the events that sent him into the past). These are mainly used in the production of Trilumnos Display In one episode, Delenn makes reference to Commander Sinclair getting the Triluminary from Epsilon III, the planet that Babylon 5 orbits which houses the Great Machine that sent Sinclair back in time. This can be seen in War Without End, when Zathras brings a number of crates aboard Babylon 4 from the White Star, including a yellow triangular-prism-shaped box which contained the chrysalis device and the Triluminary (possibly all three Triluminaries). 
Thus, the name Triluminary could refer not only to its triangular shape, but also to there being three of them, as mentioned by another Minbari of the Grey Council in Babylon Squared: "Take it, Delenn, no one will miss it...for a time... we have two others."
The Chip within the Triluminary has been alleged to be portions of the internal mechanisms of an Earth Alliance Commlink, as both devices are coded to detect an individual DNA signature, specifically that of Commander Sinclair. It has similarly been alleged by some fans that Sinclair, shortly before becoming Valen, built the Triluminaries himself, using his own commlink as raw materials. However, this is contradicted by evidence in the script for "Atonement" that the triluminaries were "received by" Sinclair / Valen "from Epsilon 3", making it clear that they were not built by him. Contrary to fan theorising, there is no canonical evidence to support the inclusion of any elements of an Earth Alliance commlink in the triluminary.