The neocortex (also known as isocortex) was the outermost layer of the cerebral cortex in a humanoid brain. This layer was responsible for higher brain functions like sensory perception and muscle control. This layer of the brain was associated with language and conscious thought.
When Deanna Troi was tormented by music planted into her mind by Kevin Uxbridge, Doctor Beverly Crusher inhibited almost all the activity in her neocortex, yet the counselor continued to hear the music. (TNG: "The Survivors")
When Captain Jean-Luc Picard was under the influence of a nucleogenic beam sent by the Kataan probe and it was attempted to interrupt the transmission, synaptic responses in his isocortex failed and the Captain nearly died before all attempts to abort the transmission were stopped. (TNG: "The Inner Light")