The Doctor's TARDIS appears from outside to be an ordinary blue British Police Box (a phone booth designed for police communications). Although it is only as big as a telephone box on the outside, the TARDIS is extremely large inside with a vast number of rooms. The show has explained that this is possible in the same way that large objects that are far away look small to the eye, and describes the TARDIS as being "dimensionally transcendental", meaning that its exterior and interior dimensions exist in separate dimensions. The vehicle "travels" by dematerializing (vanishing) from one point and, after traversing the space-time vortex, simply rematerializing (appearing from nothing) anywhere else. This peculiar device was one of the trademarks of the show, allowing for a great deal of versatility in setting and storytelling without a large expense in special effects.
In the narrative, The Doctor's TARDIS is an obsolescent "type 40" that he borrowed "unofficially" when he departed his home planet of Gallifrey - all the other type 40s have long since been decommissioned and replaced by new improved models.
Although it is supposed to blend inconspicuously into whatever time or environment it turns up in, it invariably shows up as a (British circa 1950s) blue police box. (This inspiration may have been a creative ploy by the BBC to save time and money in props, but became an in-joke genre convention in its own right, particularly since there have been very few police boxes left in Britain for some considerable time.) The rationalisation for this was given quite early in the series as a failure in a mechanism (the Chameleon Circuit) which was responsible for making the outside of the machine change to fit in with its environment. Despite his considerable ingenuity in other fields, and his ownership of a sonic screwdriver, the Doctor has been unable to fix this problem completely; the occasional temporary success has always been followed by a return to the status quo. Ironically the exterior appearance of the TARDIS has become the most unchanging feature of the show over the course of its run.
Because the Doctor's TARDIS is so old it is inclined to break down, and the Doctor has often had to give it "percussive maintenance" to get it to start working properly. We also often saw him with his head stuck in a panel carrying out maintenance of some kind or another. (This gives us the amusing paradox of a space-time machine which is considerably more advanced than anything in the Star Trek universe, but which is at the same time an obsolete and unreliable piece of junk - or as the Master once put it "you might as well try to fly a second hand gas stove!".) Efforts to repair, control, and maintain the TARDIS were frequent plot devices throughout the show's three decade run.
The Master, a re-appearing nemesis of the Doctor and fellow Time Lord, had his own TARDIS, a later model whose Chameleon Circuit was not broken. In one episode each Time Lord's TARDIS materialised within the other, which led to a very confusing state of affairs!