A brain is the central area for thought in most sentient biological entities.
Richard Harries experimented with brainwaves, he was able to have sibling rats transfer knowledge through the waves and complete tasks the other had learnt. (EDA: The Banquo Legacy)
The Fifth Doctor created an anti-dreaming device that stopped the brainwaves associated with dreaming. (DW: Snakedance)
While most brains are natural, the Rani once constructed a giant brain to absorb the mental energies of various individuals and compute the computations for a time manipulator. (DW: Time and the Rani)
In certain circumstances, the brain can be transplanted out of the biological entity into another vessel, as occured with Morbius' brain and the Cybus Industries Cybermen. (DW: The Brain of Morbius, Rise of the Cybermen)
The Ood has two brains, one being carried in their hands. There was also a giant brain on the Ood Sphere. (DW: Planet of the Ood)
The Morpho were a race of disembodied brains. (DW: The Keys of Marinus)