In the Babylon 5 story, the Narn are a reptilian-looking race with red eyes. They adhere to their traditions strictly and follow a text entitled "The Book of G'Quan." Throughout the show's episodes we witness their dynamic character, which spreads from rage and spite to lovingness and warmth. They are not telepathic.
A thousand years before the time of Babylon 5, about 1258, The Shadows instigated war for the Universe. The Narn were being used as telepaths to control Shadow vessels. The Shadows were ultimately overpowered, and all the telepathic Narn were executed to avoid a repeat of this scenario.
Returning to the Babylon 5 time period: The Narn were a strong race who had their long-time enemy the Centauri on their knees. Their revenge was probably taken a little too far: the Shadows reappeared and gave assistance to the Centauri, who then destroyed the Narn home world, reversing the state of affairs. The Centauri enslaved the Narn, forcing them to work on Centauri Prime. They hunted all that escaped this fate.
The Narn were eventually freed from the Centauri by G'Kar, a Narn ex-ambassador to Babylon 5. He suffered great torture but with the help of a pitiful Centauri named Londo Mollari (G'kar's Centuri counterpart, also ex-ambassador to Babylon 5) was able to set the Narn free.
Unfortunately, many of the Narn sects were wiped out during the conquest and enslavement. G'Kar left his people in hope that they will not seek revenge again, but rather leave their enemies to self-destruct. It was his hope that they could learn to look after themselves and rebuild their people, culture, and world.
The Narn home world is a desolate, red planet. Most of the architecture is simple underground passageways and small living quarters. The Narn love a food called "Brae." Apparently these are the Narn equivalent of Swedish meat balls.