A surgeon was a descendant of Mondasian crew members aboard a colony ship which was trapped within the event horizon of a black hole. He was affiliated with Operation Exodus, a project where he upgraded his patients into Cybermen so that they could survive the harsh conditions of Floor 1056, and so that they could eventually climb to the upper floors (notably Floor 0507 and Floor 0000) and take command of the ship.
After Bill Potts was shot on Floor 0000, she was brought to the surgeon's Conversion Theatre by a group of Patients where he fitted her with a metal heart.
Some years later, he sent Mr Razor to collect Bill and deceptively bring her to the Conversion Theatre to undergo her own operation. The surgeon showed Bill a new prototype head-piece which would inhibit her emotions, developed due to the constant pain that the Patients experienced following their conversions. Against her will, he proceeded to convert her into the first fully functional Cyberman. (TV: World Enough and Time)
Shortly afterwards, the Cybermen began rounding up the remaining citizens of Floor 1056 for conversion, which presumably included the Surgeon. Operation Exodus would continue on for centuries afterwards, with the Cybermen continuing to climb up the ship to capture more Mondasians for upgrading. (TV: The Doctor Falls)