Presumably the books themselves will fill you in on the setting and point you to resources where you can find more information. However, I've never seen them so just in case they don't, here are some online resources:
Here's the official page: http://www.bbc.co.uk/doctorwho/
Here's the section on the original series where you can find background information: http://www.bbc.co.uk/doctorwho/classic/index.shtml
Might as well throw in the Wikipedia entry: http://en.wikipedia.org/wiki/Doctor_Who
The real-world summary is that Doctor Who started as a children's science fiction serial in Britain, back in 1963. It ran until 1989, evolving into a program aimed at older audiences, was relaunched in 2005 (mostly preserving the continuity), and has been in production since then. The concept of the Doctor's Regeneration (described below) was in response to the necessity of having several different actors play the part during its long run.
If you want to see someone's take on it, my own is that the Doctor is an alien from the planet Gallifrey. His race is known as the Time Lords, though there is some evidence that they are a political/cultural division of the Gallifreyan humanoid species. He pilots a vehicle that allows him to travel through large tracts of time and space, but he seems to possess a particular fondness for Earth, especially Britain.
The Doctor is an unrepentant do-gooder who usually tries to avoid violent or brute-force solutions to problems. Compared to humans, he is extremely long-lived and his age is measured in centuries of earth-years. He possesses the ability, common to Time Lords, of Regeneration: when his body is mortally injured or worn-out he can restore himself. Rather than resurrection, this more closely resembles reincarnation: the new body has a different personality and even some discontinuity of memories. However, his core beliefs are preserved; he is the same "type of person." Time Lords normally have the ability to regenerate themselves twelve times, and the Doctor has used ten of those regenerations.
The Doctor usually travels with one, sometimes more, companions, who are often, but not always, female humans from Earth. The "Doctor's Companion" is a trope that I would expect plays a role in the role-playing game. They act as a foil to his personality, and often provide someone whom he can explain things to, and through them, the audience. Some of his outlier companions included a robot dog, a fellow Time Lord, and a mathematically talented (human-looking) boy who evolved from swamp monsters.
The Doctor's vehicle, known as a TARDIS (the name is an acronym for Time And Relative Dimension In Space), has a number of famous qualities. Originally (before the start of the series) it had the ability to disguise itself as a common-place object in whatever environment it happened to be in. The mechanism controlling that ability (the Chameleon Circuit) broke down after the TARDIS landed in a London junkyard in the early '60s. Ever since then, the outer form of the TARDIS has appeared as a blue police call box often mistaken for a "phone booth." It is also well-known for being vastly larger on the inside than on the outside. The TARDIS may or may not be responsible for the ability of the Doctor and his companions to communicate with most sentient creatures they encounter: there is conflicting evidence.
Although the Doctor occasionally performs the odd mission, he usually winds up in a location through accident or simple sight-seeing. With the alacrity of a sleuth in a murder mystery, he quickly becomes embroiled in the problematic goings-on of the locality, often involving an alien or extra-dimensional presence. Over time, he has acquired a list of recurring enemies and allies: some are individuals, some are organizations, and some are entire species.