The '"Holly Hop Drive" is a small red box that is supposed to be able to transport Red Dwarf and it's crew "to any other point in space, in a matter of seconds" as seen in the Series II finale "Parallel Universe". The crew attempt to use it but during the count-down Holly misses the number seven which is, most likely the reason why they are sent to a parallel universe where females are the traditionally dominant sex - that and his general blind spot with that number. The box appears to be a small, red/orange coloured box; On the front of the box in a yellow square are printed the words, "HOLLY HOP DRIVE". On the top are two buttons labelled "STOP" and "START". The device at very least can be credited for its simplicity.
In Super String Theory aka M-Theory there exists dozens of dimensions that we can see or sense and the Holly Hop Drive is supposed to take shortcuts through hyper space, jump space, other dimensions, and even parallel universes to travel a really long distance that would normally take a few million years with conventional star ship impulse drives. Because Holly miscounted they got stuck in a parallel universe were everyone who was male is female and vice versa. Just as the Wildfire drive from "Dimension Jump" and Backwards has a basis in the many-worlds interpretationn that is rapidly replacing the Copenhagen interpretation of Schrödinger's cat fame.
Cat could not wait to meet his female counterpart only to discover his counterpart is male and evolved from a dog just as he evolved from a cat. Arnold Rimmer runs away from his female counterpart as she was attracted to him and he had no interest in her given that her views on men are the same unenlightened ideas he has about women. Dave Lister meets his female counterpart Deb Lister and they get into a drinking contest and eventually get so drunk they wake up in the same bed. But to Dave's surprise the female Rimmer says she hopes Dave gets pregnant. Dave is confused, and Deb tells him that it is the males in their universe that have children and not the females. Arnold Rimmer says "you may very well be up the duff laddie! I might even become an Uncle!" and later on Holly meets Hilly and they both appear on screen when asked to leave and Holly has lipstick kisses all over his face from Hilly.
Later on in the series Holly has a face swap to look like Hilly and the actor playing Holly is no longer in the series until later, though he later returns.
The Holly Hop Drive is also mentioned in "Back To Earth, though noted as "back on Red Dwarf", which means throughout their nine year journey after Series VIII they must have used it or it is still an available device on the ship.