Long ago on a planet called Gallifrey, the humanlike inhabitants achieved two scientific breakthroughs. First: they invented a form of "hyperspace" travel which could take them not only to other locations in space, but backward and forward in time if they chose. Second: already having a long lifespan, they extended it further through "regeneration": if a Gallifreyan was about to die of old age, or was mortally injured, he or she would have a burst of energy which reconstructed his or her body. Only in their first incarnations were they ever children; each regeneration would appear as an adult, with all the memories of the previous lifetime, but sometimes with changes in personality and temperament. They could regenerate twelve times, giving each one thirteen lives in all. Because of these advantages, the Gallifreyans came to be known as the Time Lords. Like Star Trek's Vulcans, they were certainly more like good guys than the opposite, but not usually very passionate about taking sides and righting wrongs.
One exception was a male Time Lord whose real given name seems to have been Theta Sigma, but who preferred to call himself just The Doctor. Setting out on his own to get away from the overly regulated society of Gallifrey, the Doctor soon settled on Earth as the planet he liked best. A certain version of his biography says that, like Mister Spock, the Doctor actually had an Earth-human mother; this would confirm that Gallifreyans can intermarry with Earthlings--a fact which many female characters in the TV series wish the Doctor would give more thought to! (Still, the original premise that the Doctor WASN'T trying to get inside the pants of every lovely Earthwoman he met WAS refreshing.)
The Doctor Who universe has the same plague as the Star Trek universe: ultra-super-duper-extra-hyper-unbeatable space aliens behind every asteroid and black hole. Dealing with them, and with "only sort of unbeatable" aliens, always kept the Doctor busy. There was a long hiatus of the series; and when they finally brought it back, the out-of-control fashion for oversimplifying everything in TV and movies made the producers decide to say that all the OTHER Gallifreyans had died, leaving only the Doctor.
There, does that help?