A brain was the central area for thought in most sentient biological entities.
The Fourth Doctor claimed that a machine as efficient as the human brain would have to be bigger than London and powered by the entire European grid. A Time Lord's brain was even more complex. (TV: The Invisible Enemy)
In certain circumstances, the brain could be transplanted out of the biological entity into another vessel. This was done with Morbius' brain after his body was destroyed. His ally, Mehendri Solon, had to find a head large enough to fit the brain and only found the right match when he met the Fourth Doctor. (TV: The Brain of Morbius) On Thoros Beta, the surgeon Crozier accomplished significative results in this field, with the brain of the Mentor Kiev. (TV: Mindwarp) On Pete's World, the Cybermen there were created by having the brain transplanted from the human form into the cybernetic suit. (TV: Rise of the Cybermen)
Lady Cassandra O'Brien.Δ17 was able to survive the destruction of the sheet of skin which formed her "body" because her brain was undamaged, allowing her to constitute a new skin body with another skin sheet from her old human body — this one taken from her backside. (TV: The End of the World, New Earth)
The Clockwork Repair Droids of the 51st century spaceship SS Madame de Pompadour thought they could use the brain of their ship's namesake, Madame de Pompadour herself, to help repair their ship, to this end they opened up Time windows back to 18th century France to stalk Madame de Pompadour. (TV: The Girl in the Fireplace)