Well, this song basically gives a better backstory than I ever could, so here. That's the way back history. https://youtu.be/q2ldOzms47c
Technology[]
The Gallifreyans, or Time Lords, are extremely long lived and immensely intelligent beings that have created many different technologies, chief amongst them T.A.R.D.I.S. technology, which stands for Time And Relative Dimensions In Space. A properly maintained and piloted TARDIS can transport its occupants to any point in time and any place in the universe. The interior of a TARDIS is much larger than its exterior, which can blend in with its surroundings using the ship's "chameleon circuit". TARDISes also possess a degree of sentience (which has been expressed in a variety of ways ranging from implied machine personality and free will through to the use of a conversant avatar) and provide their users with additional tools and abilities including a telepathically based universal translation system. TARDISes are bioships that are grown from a species of coral indigenous to Gallifrey, and it can take years to complete one. They draw their power from several sources, but primarily from the Eye of Harmony, an exploding star in the process of becoming a black hole suspended in a permanent state of decay. The power source of the TARDIS (referred to as the "heart of the TARDIS") is said to be beneath the central column of the console. They are also said to draw power from the entire universe. Other elements needed for the proper functioning of the TARDIS and requiring occasional replenishment include mercury (used in its fluid links), the rare ore Zeiton 7, a trachoid time crystal, and "artron energy". Artron energy is said to be the "residue of TARDIS engines", and is also found in Time Lord brains and bodies of other time travelers. Another form of energy, "huon energy", is found in the heart of the TARDIS but nowhere else in the universe.
Before a TARDIS becomes fully functional, it must be primed with the biological imprint of a Time Lord, normally done by simply having a Time Lord operate the TARDIS for the first time. This imprint comes from the Rassilon Imprimatur, part of the biological make-up of Time Lords, which gives them both a symbiotic link to their TARDISes and the ability to withstand the physical stresses of time travel, Without the Imprimatur, molecular disintegration would result; this serves as a safeguard against misuse of time travel even if the TARDIS technology were copied. Apart from the ability to travel in space and time (and, on occasion, to other dimensions), the most remarkable characteristic of a TARDIS is that its interior is much larger than it appears from the outside. The explanation is that a TARDIS is "dimensionally transcendental", meaning that its exterior and interior exist in separate dimensions. The TARDIS has been shown to be incredibly rugged, withstanding gunfire, temperatures of 3000 degrees without even scorching, atmospheric re-entry, falls of several miles, and sinking into pooling acid. This does not apply when facing certain extremely advanced weaponry, often created after the Doctor's Type 40 TARDIS, such as Dalek missiles, for which the TARDIS requires additional shielding. The TARDIS is shown to be able to withstand immense speeds, pressure and heat by being pulled into Trenzalore's atmosphere without any functioning systems. The only noticeable damage caused was to the exterior of the TARDIS, in which a small crack is shown on the glass. This crack was gone by the end of the episode.
One of the key features of a TARDIS was that the interior existed in a dimension different from the exterior. The main application of this concept was that they were bigger on the inside than the outside. This feature required use of "dimensional dams", which, upon the death of a TARDIS, would leak through. One such effect of this was the TARDIS exterior growing to a gargantuan size.
Another feature of TARDISes was their ability to blend into their surroundings once they landed. If working properly, a chameleon circuit could assess the surroundings of a time and place just before arrival and change the exterior to resemble something common to that landscape. It also features the Reality Anchor, which immunizes it to the effects of parallel or altered reality, as well as detection via reality warping/awareness. (See: http://powerlisting.wikia.com/wiki/Reality_Anchoring)
TARDISes were incredibly complex machines. The nature of their construction was such that they were said to be grown rather than constructed. Because computers were unable to withstand the reality-changing stress, TARDISes required morphologically unstable living organic matter, or protoplasm, for their Block Transfer Computations. The outer plasmic hull, interior configuration, and a host of other details were derived from this function, as well as a TARDIS' link with the Eye of Harmony. If a TARDIS were to be used by anyone other than its owner and his familiars, it would assault their minds, which may lead to memory loss. When the TARDIS needed more power to take off, rooms could be jettisoned to provide this power. This feature was used to escape both a gravity bubble, and to provide the extra power required to leave the universe entirely.
TARDIS computer interfaces included: ◾ An Index File provided text-based research into all manner of subjects relevant to TARDIS pilots and crew.
◾ A voice interface could be requested for a variety of purposes. The TARDIS was able to communicate with its occupants using a holographic avatar, based on the Brigadier, and also created re-enactments of events from history, with characters based on the previous owners and their companions. It is also possible to gain medical analysis and limited psychological counselling from this interface.
◾ A device compatible with 21st century Earth DVDs was capable of reading and executing automated piloting instructions for a TARDIS.It also could burn software to CD/DVD media for use on Earth computers.
◾ Psychic circuits kept a TARDIS linked to its crew when they left its interior, providing translation from alien languages and perhaps other features, so long as its attending Time Lord was in good health.
These are the defensive capabilities of a TARDIS, linked to because the descriptions are far too long. Note, not all of these will be used. http://www.whoniverse.net/tardis/defence
It can also serve as a home for its pilots, and as such has many living arrangements contained in its design. http://www.whoniverse.net/tardis/environment
Another of the Gallifreyan's great achievements was Sonic technology, such as the Doctor's Sonic Screwdriver, seen here http://tardis.wikia.com/wiki/Sonic_screwdriver . The Sonic is most likely the only example of this tech that will ever be used.
Their physiology and culture can be found here
http://tardis.wikia.com/wiki/Gallifreyan_physiology
and here