The time winds were a form of temporal radiation that caused anomalies and glitches in space-time. It was "a window right through to another time, only the world on the other side [was] shifting in constant flux." (PROSE: Engines of War) They were the winds of time within the Time Vortex and intercept points such as the Gateway. They could have a detrimental effect on computers such as K9 Mark II and occasionally beings such as the Time Lords.
Certain species with time sensitivity, such as the Tharils, could walk or ride the time winds to access other times and places. The Tharils used this ability to build an empire. Humans (being a non-time sensitive species) could not do this, and they used special methods to capture and imprison Tharils so they could harness this ability. It was a painful process, as it was used on Romana, and she screamed in agony. (TV: Warriors' Gate)
The Eighth Doctor was led by Strax in France, during the Great War. A leak of time winds from the vortex - caused by Kotris and the Daleks - was causing trouble and harm to the humans. (AUDIO: The Great War)
Items could be ripped apart by the time winds within the Time Vortex, or eaten slowly away. This also applied to species which lacked abilites to weather the time winds, including Daleks. (AUDIO: The Time of the Daleks) Other forms of species could apparently live inside the Time Vortex without being destroyed by the time winds, to the Nine's surprise, (AUDIO: Relative Time) such as the Reapers, whose resilience was so great the Ninth Doctor said nothing in the entire universe could harm them. (TV: Father's Day)
Iris Wildthyme's TARDIS would let in time winds every time it entered the Time Vortex (PROSE: Verdigris), or by some accounts, The Maelstrom. The winds often caused a lot of noise, causing passengers in the Celestial Omnibus to shout. (PROSE: Enter Wildthyme) Because of these winds, Iris worried about taking off with the doors to her TARDIS slightly ajar. (AUDIO: Iris Wildthyme and the Claws of Santa)
Captain Jack Harkness was killed by the time winds when he clung to the side of the Doctor's TARDIS as the Tenth Doctor attempted to dematerialise before Jack could reach him; however, Jack's immortality brought him back to life as soon as the TARDIS landed on Malcassairo. (TV: Utopia)
Placing something next to the heart of the TARDIS or the time rotor would expose it to time winds. Clara Oswald placed a turkey under the console, which the Eleventh Doctor explained would either be cooked or lay eggs. (TV: The Time of the Doctor)
The TARDIS' exterior shell was destroyed from the time winds as it stayed in the Time Vortex for a long period of time, leaving the interior exposed and the occupants go insane. (AUDIO: Scenes From Her Life)