The cerebral cortex is the part of the brain involved in many higher level tasks such as language, memory, and consciousness. The cerebral cortex includes the parietal lobes, the occipital lobe, the frontal lobe, and the temporal lobes.
A burst of seventy millivolts will burn out the cerebral cortex of a normal humanoid brain. This, however, can be cheated with an injection of an inoprovaline drug, which provides additional resistance against such excessive electro-stimulation. (DS9: "Life Support")
Ceti eels from Ceti Alpha V enter through a Humanoid's body by the ear and wrap around the cerebral cortex, causing the victim to be susceptible to suggestion. (Star Trek II: The Wrath of Khan)
If damaged, tissue in the cerebral cortex can also be treated using a cortical analeptic. (VOY: "The Swarm")
When Deanna Troi temporarily lost her empathic sense due to the influence of two-dimensional lifeforms, a pattern of unresponsive cells in her cerebral cortex and cerebellum was recorded. (TNG: "The Loss")
The Prytt used a psi-wave device implanted in the cerebral cortex as an interrogation method. (TNG: "Attached")
Seven of Nine's cerebral cortex underwent severe stress in 2375, when a malfunctioning Borg vinculum caused numerous neural patterns from assimilated individuals to overwhelm her mind. (VOY: "Infinite Regress")