It might look like just a 1960s police telephone box from the outside, but the TARDIS is one of the most powerful vehicles in science-fiction. It represents the pinnacle of Time Lord technology, a ship that's not built so much as grown, and is capable of travelling through the space-time vortex to anywhere in time and space.
TARDIS stands for Time And Relative Dimensions In Space. It appears on the outside to be a police box because its chameleon circuit, which is supposed to disguise it as an everyday object to make it blend in with its surroundings, got jammed while on Earth in the very first Doctor Who story, An Unearthly Child. The Doctor has made some half-hearted attempts to repair the chameleon circuit, but seems to have grown quite attached to its appearance.
The TARDIS is bigger on the inside than the out - dimensionally transcendent, if you like. The main control room has changed appearance several times, and the Doctor has used a tertiary control room on occasion. The TARDIS is also known to have a well-stocked wardrobe with clothes for many different times and places, bedrooms, a swimming pool, endless corridors and a cloister room. Whether there are any limits to the inside of the TARDIS is unknown.
Back in the ancient times of Gallifrey, the ruling triumvirate Rassilon, Omega and the Other set out to harness the power of a black hole. Together, they harnessed the black hole, though Omega was swallowed up by it in the process. Rassilon took it back to Gallifrey where it was placed beneath the Citadel of the Time Lords. The Eye of Harmony, as they called it, was the power source for their time-ships. Now that Gallifrey has been destroyed in the Time War, the Doctor has to refuel the TARDIS by other means, such as the Rift in space and time that runs through Cardiff.
The TARDIS is almost alive, and power unimaginable even to the Doctor runs through the heart of it beneath the console. For the Doctor, the TARDIS is more than just a way of getting from A to B. It's his home, his last remaining link back to Gallifrey and to his people who are now gone forever. Battered, repaired and often help together by little more than sticky tape and goodwill, it is a most fitting mode of transport for that madman, adventurer and daredevil known as the Doctor.