Sky trenches were a form of airborne defence used by the Time Lords. Much as a traditional trench served as a front-line defence to prevent enemy advance, sky trenches formed multi-layered armoured shields high in the atmosphere that prevented aerial invasion.
Bennus noted that none of Gallifrey's defenses, including the sky trenches, would be able to withstand the impact of the Thousand Worlds which the Daleks planned to forcibly crash into Gallifrey at fifty times the speed of light. (AUDIO: The Heart of the Battle)
Arcadia was protected by 400 sky trenches, making it the safest city on Gallifrey. Nevertheless, Dalek forces managed to break through these supposedly impregnable defences on the last day of the Last Great Time War, leading to the fall of the city. However, while many Daleks invaded the breach in Arcadia, the bulk majority of the attacking force could not descend into Gallifrey as well, failing to penetrate the trenches surrounding the exterior of the planet. (TV: The Last Day, The Day of the Doctor)
The Capitol was also protected by sky trenches. Despite gathering their full strength, the Daleks were never able to breach these defences, even at the very end of the Time War. (TV: The Day of the Doctor)