John Doe was the amnesiac head of the Network.
Before losing his memory, Doe had known the Third Doctor, Sarah Jane Smith and the Brigadier. He did not know what caused his amnesia, but blamed the Doctor based on his fragmentary recall, and sought him for years to exact revenge.
He was made the head of the Network, in large part because the damage to his mind meant the ESPnets that worked for him could not read his mind. When he found out he had been manipulated by the Magnate, he wanted to kill all those he held responsible. Before he could start by killing Evelyn Smythe, pub owner Gary Rudge shot him dead. (PROSE: Instruments of Darkness)
Behind the scenes
It is implied that John Doe was originally Jeremy Fitzoliver, and that he accidentally erased his own mind with the Doctor's IRIS machine while UNIT was dealing with the invasion of the spiders from Metebelis III. (TV: Planet of the Spiders)