Tempus

The Name TARDIS is the abbreviation for Time And Relative Dimension In Space which in itself is a rough description of what a TARDIS really is. On Gallifrey itself, they seem to be sometimes referred to as TT Capsules but the name 'TARDIS' seems to become more and more prevalent even there. The term TARDIS would seem to have been originally coined by the grand-daughter of a renegade Time Lord called 'The Doctor'.
Function Put as simply as possible, a TARDIS is a time machine; a vehicle which allows the users to go anywhere in all of Space/Time at will. The exact method on how a TARDIS travels is unknown but it is clear that the exterior shell enters the Time Vortex and travels along it until the appropriate location is reached. The nexus of this Time Vortex is located on Gallifrey.
Shape & Form The outward appearance on a TARDIS is dictated by the Chameleon Circuit, a system designed to make a landing TARDIS as inconspicuous as possible. For example, a TARDIS arriving in Ancient Rome might take the form of a stone pillar or maybe a large water feature. Likewise, a TARDIS materializing in a forest might take the shape of a tree or a boulder.
The door of a TARDIS is actually a dimensional bridge which links the outside shell dimensions with the pocket dimension that the interior of a TARDIS exists in. It's this separation of dimensions which is one of a TARDIS' main defensive assets.
Interior The interior of a TARDIS in no way reflects its outward appearance. To start with, the interior is many times bigger than the exterior - estimates of exactly how large vary from the size of a large city to literally infinite space.
Telepathic Circuits & Sentience A TARDIS appears to be semi-sentient, being able to communicate with its pilot on a subconscious level through the telepathic circuits as well as possessing a strong self preservation instinct.
Sensors A TARDIS is equipped with an impressive sensor package, able to accurately measure all manner of variables ranging from radioactivity, gravity, heat, humidity, temporal anomalies ... even radar. The sensors would seem to tie in with the TARDIS landing routines - locating a safe out-of-the-way spot for the TARDIS to land (so it doesn't squash some poor unfortunate being for example). There is also an external visual scanner which can pan around the TARDIS and relay the images to the view screen in the Control Room.
TARDIS viewscreenDefenses & Security A fully functioning TARDIS is next to impossible to destroy; this is due mainly to the nature of its dual-dimension existence. After all, how can you possibly affect something which is located in an inaccessible other dimension? The only available target for attack is the outer shell but since that in itself is a projection of the 'real' TARDIS, it is more or less completely invulnerable in its own right. Shaking of the TARDIS interior has been seen on numerous occasions when the exterior has been attacked, this is most likely due to the dimensional bridge which links the exterior and interior together. There is only one known event which has been shown to be able to destroy a TARDIS and that was 'Event One' - and a TARDIS can even escape that by finding extra power and dematerialising away.