It appeared inside black holes as six twisted coils of energy, depending of which reality you saw it from, of a configuration and beauty almost beyond human comprehension. Holly, while having an IQ of 12,368, discovers that there are seven main Universes. Universe 3 is the only one numbered, which is described as being a mirror image to the Dwarfer's native Universe, except time moves backwards, suggesting that their own Universe is either 2 or 4. Holly believes that this Universe makes more sense than theirs. The other five Universes and their nature are unknown.
The crew first travel across it, suggested by Holly as a super-genius, in order to bury Lister, who died as an old man, in Universe 3, in order to revert his death by heart attack. In both the conflicting sequels to the novel, Doug Naylor's Last Human and Rob Grant's Backwards, they cross it again to rescue Lister (and in Last Human the now reanimated Kristine Kochanski as well) from the backwards Earth. (Better Than Life)
In Last Human, returning back, they do not return to their own primary universe as thought but to one of the parallel realties, where they find that universe's equivalent of Starbug crashed and most of their doubles dead. Learning that Lister's other self is alive somewhere from the last words of that reality's Kochanski, they set off to find him and, after locating his whereabouts, freeing him from GELF imprisonment in the penal colony of Cyberia. Lister's other self is later revealed to be much different than our own. Rather than a amiable slob, he is a sociopath with an interest in all things morbid, even to the extent of slaughtering his shipmates in order to get his hands on the power of G.O.D.. This causes great trouble for our Starbug crew after they have rescued him. The main other difference between our crew and their crew is that in that reality Rimmer is Kochanski's lover and not Lister.
After assuring Earth's destruction in our reality, the Space Corps created the genetic engineering device G.O.D. and various other terraforming or otherwise positive viruses and sent them out on the Mayflower to create humanity's new home. The ship gets lost however and crosses the omnizone itself and crashes into a planet on the same parallel reality mentioned earlier. This sets up much of the plot of Last Human, such as the introduction of Rimmer's actual son (not the son of this parallel reality's Rimmer), Michael McGruder who was on the Mayflower when it crossed into the Omnizone. (Last Human)
The novel Backwards has the Starbug crew stranded in the backwards reality for decades due to a series of mishaps. When they finally do get out and cross the omnizone they find that Red Dwarf is gone. After finding what remains of Holly's circuitry, they learn that the ship has been captured by Aginoids - lethal killer androids. All is not lost though thanks to the arrival of Rimmer's dashing heroic counterpart Ace Rimmer in the experimental cross-dimensional ship Wildfire. The Wildfire is capable of crossing not just the seven main Universes, but all parallel realities, all created from the choices people make. The Wildfire drive is used at the end of the novel by the only remaining survivors, The Cat and Lister, to escape to another parallel reality. The first reality they come across, Rimmer, Kryten and Holly are alive while Lister and the Cat died playing Better Than Life. (Backwards)