In Doctor Who, the Doctor belongs to the species known as the Time Lords.
The Time Lords are an ancient extraterrestrial people from Gallifrey, a planet in the constellation of Kasterborous. They are associated with advanced science, time travel, and the TARDIS, the dimensionally transcendental time machine the Doctor uses to travel through history and space. The Doctor is a renegade Time Lord who left Gallifrey and generally refuses the species’ traditional policy of non-interference.
Time Lords are recognizable by several unusual biological abilities. Most famously, they can regenerate after suffering a mortal injury, replacing their body and often changing their appearance and personality while retaining their memories and identity. They also possess two hearts and unusual resistance to some environmental hazards.
The species was introduced gradually. Early Doctor Who stories established that the Doctor was alien but did not name his people. The Time Lords were formally revealed in the 1969 serial The War Games, while Gallifrey was named on screen in The Time Warrior. Gallifreyans is not the best answer: it refers broadly to inhabitants of Gallifrey, whereas Time Lord is the specific species or status associated with the Doctor.