A time distortion was a disturbance in space-time, sometimes caused by anachronisms.
The Time Lords often used time distortions to project thoughts into other individuals across time. This was used once on Schmidt while the the Doctor was trapped on a German U-Boat. Commander Vansell used Schmidt to try and kill the Doctor. (The Sirens of Time)
Cyber-Technology could detect the Doctor's TARDIS by registering the time distortion it created. (TV: Attack of the Cybermen) The Sixth Doctor had a tracking device for time distortions, which he was able to track the Rani with. (TV: The Mark of the Rani)
Time distortion was present in the Humanian Era, the Sensorian Era, and the Sumaran Era, caused when the Eighth Doctor rescued Charley Pollard from the R101. (AUDIO: Neverland)
The Eleventh Doctor could not land the TARDIS in 1938 New York because of time distortions. (TV: The Angels Take Manhattan)
Behind the scenes
Time distortions in the Time Vortex act as obstacles in the first and last levels of the online game Doctor In A Dash where, as with all levels, the Doctor's TARDIS (the player) races against a Dalek flying saucer, a Judoon rocket, and a Slitheen craft to find a Space-Time Manipulator.