Triton is a moon of the gas giant Neptune, out towards the end of Earth's Solar System. Triton is by far the largest of Neptune's natural satellites and the only large moon in the Solar System with a retrograde orbit - that is, it rotates in opposition to the planet it orbits.
By the time the JMC mining spaceship Red Dwarf left the Solar System at some point during the mid-to-late 22nd century, Triton was the outermost planetary body in the Solar System with a permanent human population, and was also the coldest such body. Further-out Pluto had not yet been colonised by the Space Corps. As such, Triton's early settlers were of an adventurous nature, and at the time that Dave Lister enlisted with Red Dwarf Triton was still in its formative stages, with construction of the colony outside a central core still underway.
Triton is mentioned very little in the television series, but mostly mentioned in the additional materials on the official Red Dwarf website and the novels.
Alcoholic Red Dwarf cook Olaf Petersen had once bought an abandoned military base on Triton, intending to turn it into a distillery for his "Petersen's persuasive". Petersen got tired of Triton very quickly, and later jumped ship to Red Dwarf when it passed by, hacking the terminals to enlist himself with the JMC.
Centuries later, renowned Solar System scientist Nirvanah Crane spent some time at a research base on Triton, and was possibly born there. Crane later died on Pluto, which had then since been colonised, but Pluto was destroyed in a nuclear explosion. Crane was resurrected as a hologram to serve aboard the Enlightenment.