"Look around you...I have transplanted myself into every human being!" - The Master
The Master Race were created when the Master stepped into the Immortality Gate and transferred his genetic template to the 6,727,949,338 human beings on Earth changing them into himself.
When the Master used 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 versions of himself.
Just a few humans avoided this transformation. Wilfred Mott, who was protected by special radiation shielding at the time, Donna Noble who gained a Doctor/Donna connection by travelling with the Doctor. Sarah Jane's adopted son Luke Smith also appeared to not transform as he was made by the Bane. Aleins who were on Earth at the time, were unnafected by this.
With many important humans transformed, such as President Obama, and many UNIT officers, the Master planned to use them to attack the rest of the universe. When the Master realized that the new Master race had inherited the drumming noise in his head, he used it to create a link between him and the trapped Time Lords in the Time Locked Time war. 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.
The Master attempted to transform the Time Lords into him, but Rassilon would reversed the Master's transfer of genetic code with a wave of his hand, the human race returned to their true human form.