The Great Key of Rassilon was one of the Artefacts of Rassilon. It was rarely in the possession of the Lord President. The Chancellor typically held the Great Key. A forbidden weapon known as the De-mat Gun was activated by the Great Key. (TV: The Invasion of Time)
Following the Great Key's creation and the development of Gallifreyan society, Rassilon entrusted the Great Key of Rassilon with the chancellor; if the Lord President were to have the Sash, Rod and Great Key of Rassilon, he would have absolute power, therefore it had to be kept out of the President's hands to prevent a dictatorship. No record of this was mentioned in the Matrix.
Following signing a treaty with the Vardans, the Fourth Doctor travelled to Gallifrey and declared his intentions to become Lord President, a declaration which was unchallenged; as part of his oath, the Fourth Doctor was tasked with finding the Great Key of Rassilon. According to Borusa, though every President similarly took the same oath, none had ever found it prior to this encounter. The Doctor revealed that everything he was doing was all an act to find the Vardans' planet of origin and place it in a time loop.
Following the defeat of the Vardans and the subsequent invasion by the Sontarans, the Doctor refused to let them have the Great Key and interrogated Borusa for its whereabouts, tricking him into revealing he had it. Though Borusa attempted to deceive him by first claiming that it was merely a legend, then handing the Doctor a fake, Borusa eventually was forced to give him the genuine article, telling him that he was the first President since Rassilon to hold the Great Key. The Doctor later gave it to Leela to look after briefly, an act Borusa strongly disagreed with but the Doctor assured him she wouldn't let anything happen to it.
The Doctor later had Rodan build a De-mat Gun while under hypnosis, which was armed using the Great Key. He erased the Sontaran accompanying Castellan Kelner before using it on a bomb that Stor planned to use on the Eye of Harmony. This obliterated Stor and cancelled the bomb's explosion but also destroyed the de-mat gun as well as erasing the Doctor's memory of his actions on Gallifrey. (TV: The Invasion of Time)
During the Last Great Time War, the Eighth Doctor infiltrated a prison on an unknown planet as a prisoner to steal the Great Key when it arrived on a transport. After over a month of imprisonment, the Doctor escaped with his cellmate, a Malmooth named Chantir, and successfully stole the Key. When Chantir asked if the Doctor would create another De-mat Gun with the Key, the Doctor replied that he intended to create something of similar properties on a larger scale. (COMIC: The Forgotten) According to one account, the Doctor created the Moment with the Great Key. This wiped out millions from time and space at once and ended the Last Great Time War. (COMIC: Don't Step on the Grass)