The TARDIS is a time machine and spacecraft - the name being an acronym for Time And Relative Dimension In Space. Properly maintained and piloted, a TARDIS can transport its occupants to any point in time and space. Dimensionally transcendental (the interior is much larger than its exterior), it can blend in with its surroundings using a 'chameleon circuit'. It also provides its users with additional tools, including a telepathically based universal translation system.
Interestingly, the best known version of the ship is that owned by The Doctor - an obsolete Type 40, Mark 1 TARDIS. Its chameleon circuit is broken, so it's stuck in the shape of a 1960s-style London police box. It's meant to be piloted by a crew of six, which makes life a bit tricky if you are trying to fly it on your own. And the ship itself is unpredictable - although it is later revealed that the TARDIS takes The Doctor 'where he needed to go' as opposed to where he 'wanted to go'.
Doctor Who is, of course, a British science-fiction television programme produced by the BBC from 1963 to the present day. The show is such a part of British popular culture, that the TARDIS is now much better known that the Police Box that shares its image.