The Cyber Park, also called a Pleasure Park, was the most advanced artificial reality suite ever devised. It was created by the gestalt entity known as Legion aboard his space station complex, during the time that Legion was composed of the greatest minds of the 23rd century, among many other inventions such as the Star Drive and the "hard-light" hologram.
Three million years later, the boys from the Dwarf were brought aboard the Legion Station when Starbug was ensnared by it. Reformed from their personalities, Legion attempted to convince them to stay to ensure his own existence. One of the ways he attempted to do this was by recreating their perfect sleeping quarters.
Legion also offered Dave Lister use of his Cyber Park when Lister complained about having no company. Legion stated that within the Cyber Park, Lister could go to any time period he desired, and indulge in any fantasy he wished, with any persons he desired.