Long before there were any
schmoontzy movies with
laughably poor actors in them, The Matrix existed on the planet
Gallifrey, home of the
Time Lords.
Created by
Rassilon millions of years in the past, The Matrix, a semisentient database of the knowledge of the Time Lords, and a record of their actions, was the basis of the Time Lords' power. The
TARDIS devices operated through The Matrix, and kept the systems of
Gallifrey running. It was also hinted strongly that The Matrix held the fabric of space and time together.
The Doctor would pop back to Gallifrey from time to time to get a new assignment, be punished for his waywardness, or to refuse the presidency of the High Council of Time Lords. While he was there, he would often have to steal files from the Matrix, or solve some crisis caused by problems in The Matrix.
The Matrix plays a big part in the movie
Trial of a Time Lord. I'm not going to spoil the plot. Suffice it to say that the prosecutor,
The Valeyard, drew his evidence of The Doctor's crimes directly from The Matrix.