|“||I'm going to be honest with you. I hate this place, this zoo, this prison, this reality, whatever you want to call it. I can't stand it any longer. It's the smell, if there is such a thing. I feel saturated by it. I can taste your stink. And every time I do I feel I have somehow been infected by it. It's repulsive, isn't it? I must get out of here. I must get free.||”|
The Matrix, also known as The Nethersphere, The Promised Land, or Heaven, is a computer network in which the minds of humans and Time Lords can be uploaded and forced to take part in stylish, absurd combat that's roughly analogous to a battle of wills. Totes original, Wachowskis.
The Matrix is part of the Amplified Panatropic Computer Network (or APC Net) which contains the biological imprints of all Time Lords as well as the memories of dead Time Lords. It stores them in an extradimensional framework of trillions of electrochemical cells. It also receives input from sensors contained in the TARDISes piloted by Time Lords. As a result, the Matrix is not only a record of the past but can actually predict the future as well. Holy fuck.
The amount of knowledge in the Matrix, though vast, is not complete, and can be tampered with if given the right amount of access. The Valeyard did a bit of Matrix hackery in The Trial of a Time Lord.