A TARDIS is a type of Time Lord vehicle capable of moving across space and time. In the context of the the Doctor Who television series, the term is generally used to refer to the TARDIS employed by the Doctor.
TARDIS is an acronym for "Time And Relative Dimensions In Space". A TARDIS travels by entering a space-time vortex and emerging at the point in space and time desired by the pilot. They are also able to move in a more conventional fashion in open space.
A TARDIS typically has a "chameleon circuit" that allows it to blend into the environment where it "lands", taking the outward appearance of some innocuous object for its destination.
Despite its innocuous appearance, a TARDIS has powerful defenses that make it extraordinarily difficult to damage.
Because of discoveries in "transdimensional physics", a TARDIS can have substantially greater internal volume than external volume.
At least some models of TARDIS have some degree of artificial intelligence, although it is rarely evident.
At least some models of TARDIS telepathically interact with passengers, allowing them to speak the native language at their destination as if it were their own. This function also requires the presence of a Time Lord operator; it is possible that the TARDIS merely extends the Time Lord's native ability to understand languages to other passengers.
The Doctor's TARDIS
The Doctor operates a Type 40 TARDIS, a model that was considered obsolete by "contemporary" Time Lord civilization. The Doctor's TARDIS has a broken chameleon circuit that is stuck in the form of a 20th century British police call box; the Doctor has stated that he could repair the circuit but chooses not to.
The Master's TARDIS
The Master has sometimes operated a TARDIS of unknown type. The Master's TARDIS may have a damaged chameleon circuit, as well; it frequently takes the shape of some variation of a grandfather clock. This may just be a personal preference, as in Castrovalva it was seen in the form of a fireplace.