They are a humanoid species with large amounts of yellow to reddish-brown spotting on their heads, arms and bodies. They have pale skin and a plume of ginger hair across the top of their heads. Adult males also have ginger whiskers growing on either side of their face, which, when tugged induce sexual arousal.
The Talaxians, or the Talax-Ilzay as they were known in their old tongue, were quite an ancient spacefaring race who had developed warp drive by the 1450s, where they were first contacted by the Vaadwaur. (VOY episodes: "Caretaker", "Dragon's Teeth")
By the 2340s, the Talaxians were involved in a lengthy war with the Haakonian Order. The war was so costly to both sides that many Talaxians fled to other regions of the Delta Quadrant; one group even managed to settle on an asteroid on the Delta/Beta Quadrant border by 2377. The war between the Talaxians and the Haakonians ended in 2355 when the Metreon Cascade weapon was deployed on the Talaxian moon of Rinax, killing millions instantly. As a result the Talaxians declared an unconditional surrender. (VOY episodes: "Jetrel", "Homestead")
In the alternate reality of the mirror universe, the Talaxians also existed, as natives of Talax, in the Delta Quadrant. The Haakonian Order also attempted to decimate them in the parallel universe, but in a reversal of the primary universe history, the Talaxians were able to completely overcome the Haakonians by stealing metreon cascade technology after Haakon first used it against them. Although the Talaxian population was decimated and scattered, as they were in the primary history, they used the cascade to vicious effect against the Haakonians, causing that civilization to completely fall. (Decipher RPG module: Through a Glass, Darkly)
Neelix was one such mirror Talaxian. He ended up being stranded in the Alpha Quadrant by the Caretaker, and was taken in by the Klingon-Cardassian Alliance as a decoy to be used in their attempts to invade the prime version of reality. To this end, Alynna Nechayev employed the mirror Neelix aboard Voyager, a replica of the USS Voyager built to fool the crew of the USS Enterprise-E into thinking that their universe's Voyager had returned home. (ST - Mirror Universe Trilogy novel: )