In the very first episode, Susan, the Doctor's Granddaughter claims that she made up the name TARDIS from the initials: "Time And Relative Dimension In Space." In later stories, it stands for "Time And Relative Dimensions
In Space". In early episodes it was also referred to as "The Ship" and in some stories as a "time capsule". The Doctor has also been known to refer to his time machine fondly as "Old Girl".
The TARDIS is a Type 40 time capsule - an outdated design by Time Lord standards. When the Doctor escaped his home planet of Gallifrey, he "borrowed" it and has been using it to travel endlessly through time and space ever since. The TARDIS is rather old and temperamental, often breaking down, rarely landing in the right place, and frequently described as having a mind of its own.
In order to travel through time and space, the TARDIS must first dematerialize, and enter the Temporal Vortex. This will allow it to move through the Space Time Continuum before rematerializing at any required point in space or time - in theory.
The exterior of the TARDIS is constructed from a plasmic outer shell, which should be able to change form to fit its surroundings. However, when leaving 1960s London, the chameleon circuit broke, leaving the outside of the time machine irreparably stuck in the shape of a Metropolitan Police box. It seems able to change into different types of Police boxes, but nothing else. The exterior is also protected by a powerful force shield, rendering it virtually indestructible.
The interior is much larger than might be expected. This is because the TARDIS is "Dimensionally Transcendental" meaning that the inside and outside exist in separate dimensions. Confused? Well, it's Time Lord stuff really. To put it simply: it's bigger on the inside than on the outside. Just how big has never been made clear. To learn more about the inner and outer workings of the TARDIS, see the "Useful TARDIS Links" section below.