The Time Lords were the inhabitants of the planet Gallifrey and one faction involved in the Last Great Time War.
History
The Doctor and the Master were both Time Lords. (TV: Deadly Assassin (TV story) The Deadly Assassin et al.)
The Time War
The Time Lords fought the Last Great Time War against the Daleks. Years were used as ammunition which resulted in individuals such as the Doctor being Doctor's age aged to five million and then back to a baby in the Battle of Rodan's Wedding.
Eventually, according to one account, the Eighth Doctor turned to the Moment, his mind made up to use it to wipe out both the Time Lords and Daleks to put an end to the War. As Gallifrey was destroyed around him, the Doctor fell through space and into the open doors of his TARDIS, breaking his bones in the impact.
He believed that using the Moment had made his existence fixed, preventing him from regenerating, only for regeneration energy to begin engulfing him; he belatedly realised that a woman who had died saving him had passed on the Restoration to him, resetting his life-cycle. Shocked and exhilarated, the Eighth Doctor regenerated into the Ninth Doctor, (PROSE: Doctor Who and the Time War) becoming the last of his race (TV: The End of the World) to the best of his knowledge. (TV: (TV story) Utopia)