When the colony ship almost traversed into a black hole, each of the ship's floors was affected by time dilation. Located at the lowest end of the ship, time travelled more normally on floor 1056 than on any of the floors above, where it was slower. 2 days and 10 hours at the top equated to just over 1000 years for those on floor 1056.
The ship was travelling from Mondas to pick up colonists. When the ship almost traversed into a black hole, around twenty crew members were sent to the bottom of the ship, approximately to the location of floor 1056, to reverse the rear thrusters. Unable to return to the top of the ship, the crew members remained at the bottom. (TV: World Enough and Time)
Many generations later, the deck was rusting away and the air was filled with fumes from the ship's engines. The staff at the hospital on floor 1056 were working towards Operation Exodus, an artificial evolution which would aid the survival of the floor's inhabitants. At some point, the Master crashed his TARDIS on the floor, damaging the dematerialisation circuit in the process. The Master took over the city for awhile, but the residents grew tired of his cruelty and overthrew the Master, forcing him into hiding. He eventually hijacked the hospital and placed it under his control, having the people gradually upgraded into prototypes. The Master programmed these stronger-than-human prototypes to travel to the upper levels to collect any remaining humans for conversion.
Over the years, the technology grew more advanced and Bill soon became the first fully cybernetic humanoid. (TV: World Enough and Time) After the Twelfth Doctor altered the Master's controls to have the Cybermen convert two hearted beings as well as humans, they fought off the army of Mondasian Cybermen until Nardole collected them in a shuttle pod so they could evacuate. Over the next several hundred years. The Cybermen upgraded further, committing to Operation Exodus to eventually take control of the entire ship, sending numerous evolved models to higher floors to do so. (TV: The Doctor Falls)