Bio-printers are based on the 3D printers of the early 21st century, although bio-printing uses biological matter instead of metals/plastics.
The bio-printer holds the code for the genetic material of the donor in its digital database, printing it onto sheets of artificial stem cells - "synthi-cells" - to rapidly create a near-perfect clone of the original.
However, bio-printed clones are not considered technically human, merely "human-like". Bio-printed clones are also fairly susceptible to damage, and will normally collapse into a pile of goo once a pre-programmed task has been carried out.
Bio-printing came into common use some time in the mid-to-late 22nd century. During his youth in Liverpool, Dave Lister sold the rights to his unique genome to his mate "Dodgy" for $£100 and half a packet of fags. Three million years later, Lister would learn from a recently recovered bio-printer that thousands of companies had taken out a license on Lister's DNA. Lister realises that all those "smart-arse Scousers" in call centers, who "know nothing" and "all sound like they do not want to be there", were actually copies of himself.
Three million years into the future, the unmanned Space Corps exploration spaceship SS Nautilus, which had originated in the 24th century, came into trouble. With its engine burnt out, it was drifting close to an asteroid storm, and was carrying explosive nuclear waste aboard. In an automated emergency procedure, a bio-printer aboard the Nautilus - registration 745 - began to print out a copy of its old captain, Edwin Herring. However, the old machine was faulty and it jammed, resulting in a badly deformed clone with its face printed on top of an elongated head.
The boys from the Dwarf happened to be cruising close by in Starbug, and Captain Herring contacted them for assistance. Realising that Starbug was in danger, Rimmer launched a mining torpedo at the Nautilus, which ironically actually saved the Nautilus by pushing it out of danger. Thinking that the act was deliberate, Captain Herring promoted Rimmer from second tech to first lieutenant. After the skutters had unloaded the cargo of the Nautilus, Herring declared his mission complete and collapsed into a pile of goo.
Rimmer used the bio-printer from the Nautilus to create dozens of clones of himself, all officers, so that he could order them about. He also had a new Officer's Club built to accommodate them. However, the plan went horribly wrong when a massive printer jam resulted in the creation of the Rimmer Monster, a horrible mash-up of mutated clones. Rimmer was forced to resign from his promoted position, in order to attain the help of his crewmates in destroying the Rimmer Monster. (Officer Rimmer, Series XI)
The fate of the bio-printer is unknown, although it was presumably destroyed by the crew after the creation of the Rimmer Monster, if the machine was still in any working order after the accident.