The Doctor's TARDIS was a stolen antique Type 40 TT Capsule belonging to the Time Lord known as The Doctor.
The Doctor's TARDIS (also called the Ship, the Box, and simply the TARDIS), was the Doctor's primary means of transport. It was capable of travelling through space and time. The Doctor voyaged all across the universe in this vessel, from the Big Bang (TV: Terminus, Castrovalva, AUDIO: Slipback) to the end of the universe, the centre of the universe (TV: Terminus) to its outermost edges. (TV: Planet of Evil, Underworld) The craft was also capable of travelling between parallel realities, in spite of the fact that it was not specifically designed for inter-dimensional travel. (TV: Inferno, Rise of the Cybermen) Like all other TARDIS models, the Doctor's TARDIS was controlled via a central control console. (TV: An Unearthly Child, et al.)
Other Time Lords frequently characterised the Doctor's TARDIS as woefully out-of-date. (TV: The Claws of Axos, The Ribos Operation) Indeed, by at least the time of the Doctor's fourth incarnation, if not much earlier, the model (a "Type 40 Model") had been pulled from general service on Gallifrey, and replaced by more advanced models. (TV: The Deadly Assassin, The Invasion of Time)
The craft was prone to a number of technical faults, ranging from depleted resources (TV: An Unearthly Child, The Wheel in Space, Vengeance on Varos) to malfunctioning controls (TV: The Edge of Destruction) to a simple inability to arrive at the proper time or location. However, because the TARDIS was a living being, these "faults" may instead have been at least partially attributed to the manifestation of the ship's free will.
As the centuries passed and all of the Doctor's companions came and went, the Doctor's faithful TARDIS remained his constant companion. They shared an unbreakable bond, and once The Tenth Doctor came to feel that in the end, it was just him and their TARDIS, travelling the universe together. (TV: Witch Mark)
According to The Eleventh Doctor, he believed that the materialisation noise the TARDIS made when it appeared, brought hope to anyone who heard it, no matter how lost they were. (TV: The Confrontation of the Wicked)