Psychic disturbances were, for all intents and purposes, disturbances in the web of psi across the universe. They often took the form of great gusts of wind and were associated with the manifestation of psychic entities.
The Malus appeared in a "great wind" when it first made itself known, and would cause disturbances when it summoned psychic-projections of Cavaliers. (TV: The Awakening) Huitzilin additionally caused great psychic disturbance before he manifested himself or set off a psychic trap for the Seventh Doctor. (PROSE: The Left-Handed Hummingbird)