Anti-gravity, also known as anti-grav, was the process of creating objects free from or releasing objects from the force of gravity.
Time Lord technology
TARDIS corridors normally used anti-gravity, as the corridors went vertically as well as horizontally. House disabled the anti-gravity in the corridors of the Doctor's TARDIS in an attempt to kill Amy Pond and Rory Williams. (TV: The Doctor's Wife) Air corridors projected by TARDISes had the option to use anti-gravity, allowing the occupant of the corridor to float through the corridor instead of walk. (TV: The Time of Angels)
When the Eleventh Doctor attempted to get into Trenzalore, his TARDIS wouldn't let him and shut itself down nearby, everything apart from the anti-grav. The Doctor pulled out his sonic screwdriver and shut it down, which resulted in the TARDIS falling into Trenzalore. (TV: The Name of the Doctor).
A phenomenon occured in a Korven Space-Time Manipulator located in Gryffen Manor, involving a white hole and a black hole moving together. This was part of Thorne's plan for the Korven invasion of Earth, as Alistair Gryffen would be forced to use the temporal stabiliser on the STM, which would allow the Korven invasion force through. Had Gryffen not used the stabiliser, the holes would combine, creating a stupendous vortex of anti-gravity, with anything within its reach being sucked into oblivion, this would have resulted in the entire Earth being sucked into the vortex. (TV: The Eclipse of the Korven)
The Anti-Grav Olympics were a version of the original Earth Olympic Games active in the mid-21st century. In 2074, the Eleventh Doctor rode a anti-gravity motorbike in the Anti-Grav Olympics and finished last. (TV: The Bells of Saint John)