The TARDIS stands for `Time and Relative Dimension in Space`. The TARDIS is supposed to change its appearance according to where it is. The device that allows it to do this is called `The Chameleon Circuit` but its malfuctioned. It was never repaired. The copyright to the Police Box belongs to the BBC, having brought the copyright off `New Scotland Yard`, the headquarters of the London (Metropolitan) Police Force.
The ability of the TARDIS to travel in time is due to the power source called `The Eye of Harmony` created by the Gallifreyan scientist `Omega`. How it works isn`t clear but it is understood that... Omega would detonate a star using a stellar manipulator called `The Hand of Omega`, bring it back to Gallifrey and then use the immense forces of the crushed star to power the time travel experiments. Omega was betrayed by Rassilon, the founder of the Time Lord Society. Omega`s ship was sucked into the explosion and believed to be dead. He had in fact been sucked into an anti-matter universe. (This is mentioned in the The Three Doctors adventure.) The follow-up episode The Arc of Infinity
The Tardis is famous for being bigger on the inside compared to what it looks like on the outside. The inside of the Tardis is accessible from the outside through the Police Box front door. When the Doctor regenerates, the inside of the Tardis also regenerates. The controls for the Tardis stay in the same place but the environment and look and feel changes. The picture below is what the Tardis control room looked like when Matt Smith was the Doctor.
The ship is supposedly infinite in size but that`ll make it as big as the universe. In Journey To the Centre of the Tardis, we see the power source at the heart of the Tardis, a massive star. The Tardis is able to hold the energy inside and shrink it so that the ship can appear as a police box.