The Time Lords are in general an aloof culture. Since perfecting the science of time travel, they have withdrawn, bound by the moral complexity of interfering in the natural flow of history. However, due to corruption or good intentions of some individual Time Lords, this restriction is often secretly violated (compare with the Prime Directive), and the show occasionally referred to a Celestial Intervention Agency, which was a shadowy organization which sometimes ordered the Doctor to change history.
Over the course of the show's thirty year run, it was never made entirely clear what purpose or mission the Time Lords served, or what exactly they did with their mastery over time, nor was it ever explicity made clear what had caused The Doctor to separate from his people.
In the narrative, Time Lords have the ability to regenerate their bodies when their current body or "incarnation" has become too old or is mortally wounded. This process results in their body undergoing a transformation, gaining a new physical form and a somewhat different personality. Each Time Lord is limited to twelve regenerations, though the Master has exceeded this limit through various means. It appears possible for some Time Lords to change bodies without undergoing a regeneration before settling on the regenerated body that they want, as in the case of Romana. Several Time Lords have become renegades for various reasons, the most notable being of course the Doctor.
The nature and history of the Time Lords was gradually revealed as the television series progressed. Each story to feature them and their home planet added a layer of complexity and intrigue. This stems from the dissatisfaction of various scriptwriters with the thorny problem of why the Doctor is in exile from his people in the first place. Among other things, Time Lords are increasingly revealed as being corrupted by their inaction.
It is hinted that the terms "Gallifreyan" and "Time Lord" may not be synonymous, and Time Lords are simply that subset of Gallifreyans who have achieved the status of Time Lord via achievement in the Gallifreyan collegiate system. Time Lords are divided into various colleges, such as the Patrexis college and the Prydonian college (to which the Doctor belongs), which seems to have ceremonial and possibly political significance.
The political leadership of the Time Lords includes the President who keeps the cermonial relics of the Time Lords, and the Chancellor who appears to be the administrative leader of the Time Lords. In addition there is the Castellan of the Chancellory Guard who the Doctor has referred to as the leader of a trumped-up palace guard. There is also a body of officials called Cardinals which form the Time Lord aristocracy.
The Time Lords are normally held to be some of the technologically powerful beings in the Doctor Who universe, although there are a number of notable exceptions such as the (now extinct) Osirans and the various higher powers of the universe such as the Black and White Guardians. The power of the Time Lords appears limited by their generally aloofness from the universe and with sometimes intense internecine division between them.
While most of Time Lord history is kept as tightly under wraps as possible it is known that some millions of years ago the planet was home to a civilisation that could see all of the future and past, and that it was dominated by a cult of the Pythia, a great and powerful being. This cult was overthrown by a group of three younger Gallifrians, Rassilion, Omega and "The Other" whose name has been lost to time (Many of the novels, especially Lungbarrow and The Infinity Doctors, have stated the Doctor may be The Other reborn. The truth of this matter remains uncertain).
When these three drove the Pythia away she cursed the people with sterility and so ended that world. Forced to find a new way to live, Rassilion built the Looms, a sort of cloning device which could create new Gallifrians to replace the dead. Omega threw himself into time travel experiments. The Other's role is unclear but he seems to have held it all together and definatly had a hand in "The Hands of Omega".
The Hands of Omega were steller manipulators able to rework stars into new forms and create a source of energy necessary for time travel. Only one star in the known universe was sufficient, a star named Qabba. This was the last remaining of the first generation of stars to shine in the univese. Omega reached it just in time to make what he needed but it was not an event that would go all his own way and would take a terrible toll.
The concept of the Timelords was also adopted by the techno-sampling outfit the KLF for their hit single "Doctoring the Tardis".