This article needs to be renamed, but what to? Neither "time brain" nor "giant brain" are actually uttered even once in the serial. No name is actually given, in fact. Brain (Time and the Rani), or keep time brain (uncapitalised) and mark it as conjecture?
Talk about it here.
The Time Brain was a giant brain created by the Rani. By using the minds of geniuses from across time and space, the Rani planned to use the brain to do the calculations needed to create a Time Manipulator with which she could reshape the universe to her liking. One of the items on her agenda was to revert Earth to the age of the dinosaurs so that they could realise their full potential. Her plans were stopped when the Seventh Doctors' brain was added, stopping the Rani from controlling it.
Individuals used to create the Time Brain included Albert Einstein, Louis Pasteur, and Hypatia. (TV: Time and the Rani)
Behind the scenes
In the Children in Need sketch Dimensions in Time, the Seventh Doctor uses the term "time brain" to describe the brain of a Time Lord.