The Doctor’s TARDIS is a Type 40 time travel capsule. In Time Lord terms, it is an old and outdated model, even though it remains extraordinarily capable as a machine that travels through both space and time.
The Type 40 designation refers to the TARDIS model rather than to its blue police-box appearance. The Doctor’s particular capsule is also identified as a Mark III. Its exterior is stuck in the form of a British police box because its chameleon circuit no longer works properly, preventing it from disguising itself as other objects.
The TARDIS was originally designed to be larger inside than outside, a feature that became one of Doctor Who’s defining ideas. Its name is an acronym for “Time And Relative Dimension(s) In Space.” The Doctor acquired his capsule from Gallifrey and took it while leaving his home world.
The Type 40 is sometimes confused with other model numbers mentioned across Doctor Who’s expanded lore. Those references do not change the standard identification of the Doctor’s familiar TARDIS: it is a Type 40, Mark III capsule. Its apparent antiquity is also a recurring joke, since the supposedly obsolete machine repeatedly outperforms newer technology.