Temporal interferometry was a method of time travel.
As explained by the Eighth Doctor, it was similar to optical interferometry. Instead of light waves being broken up and recombined to get clearer images, temporal interferometry worked by obtaining a focus on a specific point in the past or future, breaking up the signals, and recombining them. A machine using these principles could bring the time period to the time traveller, instead of the normal method of the traveller going to the time period.
The Doctor said that though the theory was sound, research into temporal interferometry had proved to be a dead end. This was because it was an incredibly delicate process, and any variation could have disastrous consequences. A machine that might function on one planet might not work correctly on another due to variations in gravity or the planetary magnetic field. He said that it could "run time through the equivalent of a meat grinder."
A temporal interferometry machine arrived in Victorian England by unknown means. It was discovered by Micah Scale and later stolen by Sebastian Chiltern. Due to miscalibration, it splintered Constance Jane mentally and Octave and Nathaniel Chiltern physically. Jane went through it again and was able to undo the damage to herself. The Doctor then entered it and his Time Lord nature disrupted and destroyed the machine as he had intended. (PROSE: Camera Obscura)