The TARDIS is the name for the machine used by Dr Who for travelling through space and time. TARDIS is an acronym for Time And Relative Dimensions In Space. The Doctor's TARDIS is an obsolescent "type 40" that he borrowed unofficially when he departed his home planet of Gallifrey; all other type 40s have since been decomissioned and replaced by later models.
Although it is supposed to blend in inconspicuously in whatever time or environment it turns up in, it invariably shows up as a (British circa 1950s) blue police box. (This was probably a 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 of these left in Britain for some considerable time). The rationalisation for this was given quite early in the series as a failure in the mechanism (the Chameleon Circuit) which enabled the machine to do the adaptation. Despite considerable ingenuity in other fields, and ownership of a sonic screwdriver, The Doctor has been entirely unable to rectify this problem.
The TARDIS quite large on the inside, while on the outside it of course is the size of a callbox. The Doctor explains that it does this in the same way that large objects that are far away look small to the eye. Suspension of disbelief becomes a more important dramatic element when budgets are tight.
The Master, a re-appearing nemesis of the Doctor and fellow Time Lord, had his own TARDIS whose Chameleon Circuit was not broken. In one episode each Time Lord's TARDIS materialised within the other, which lead to a very confusing state of affairs.