The Master Race was created when the Master stepped into the Immortality Gate and transferred his genetic template to 6,727,949,338 human inhabitants of the planet Earth on Christmas Day 2009, excluding two humans that were protected against the transformation.
As the Master Race, every human on Earth was rendered identical in every way to the Master with no apparent gender or age differences. Wilfred Mott wondered if dead bodies were affected; the Tenth Doctor's reaction suggested they were.
When the Master stepped into the Immortality Gate, an alien artefact reverse-engineered by billionaire Joshua Naismith, it sent out his genetic structure to nearly every human on Earth, turning everyone into exact copies of him. Several individuals escaped this transformation: Donna Noble, who appeared to have been protected by the influence of her DoctorDonna transformation; and Wilfred Mott, who was protected by special radiation shielding at the time.
With all humans, including US President Barack Obama and the leaders of UNIT, now essentially the same man, the Master ordered his self-proclaimed Master Race to take control of the planet with the original Master as their undisputed leader. He planned to convert the planet into a warship. After the Tenth Doctor's escape, the planet's military resources were dedicated to searching for him.
Once the human race had all become the Master, they all heard the incessant drumming that had driven him mad over the years. Soon after, the Master realised he could use the combined mental power of the Master Race to send a signal of the drumming through time and space and help the Time Lords return to the universe. They made contact, and a White-Point Star diamond was sent to Earth. The Master Race recovered it and used it as a power source to pull Gallifrey out of the Time War to manifest near Earth, threatening the planet with destruction. Rassilon and other Time Lords appeared near the Immortality Gate.