Candy giver: Well, hello, and who are you supposed to be?
Me: I'm the Doctor.
Candy giver: A doctor?
Me: No, the Doctor. Doctor Who.
Candy giver: Doctor what?
Candy giver: What TV show?
Me: Doctor Who.
Candy giver: I don't know. St. Elsewhere?
Me: *sigh* Yes. I'm Howie Mandel.
Candy giver: Oh. great costume. You look just like him.
The recent revamp of the series has brought the series a little further into the mainstream, but I still don't know that I'd attempt another Doctor Who-themed costume at a party unless I had a really good idea of the kind of people who would be there. The Abbott-and-Costello bit can get old.
Anyway, here's the basic nuts-and-bolts of Doctor Who for those who are less familiar:
1. He's an alien. A Time Lord from the planet Gallifrey.
2. He can travel through time using a special ship called a TARDIS (Time And Relative Dimensions In Space) that is disguised as a blue police box. It's bigger on the inside.
3. The Doctor is not immortal exactly, but he has managed to stay alive through a process called regeneration, in which he goes through a physical transformation - often accompanied by a personality change and other changes - but retains his memories. (This allows the BBC to periodically replace the lead actor of the series as needed.) We, the viewing public, are aware of eleven different (canonical) generations of the Doctor.
4. He's a good guy.
Much of the Pertwee tenure as the Doctor had him exiled on Earth by the Time Lords for essentially being a good guy. (The Time Lords have a rule about non-interference.) Oh, yeah, and he was driving a stolen TARDIS.
These episodes had the Doctor working with the United Nations Intelligence Taskforce, a military operation tasked with paranormal and extraterrestrial investigation, and were the first Doctor Who episodes shown in color. Eventually the exile was lifted and the Doctor set about traveling the universe again.
This was also the Doctor who introduced the now cult-favorite line "reverse the polarity of the neutron flow." Something that made the Third Doctor different from his other incarnations was his knowledge and practice of the martial art Venusian Aikido (sometimes called Venusian Karate.) The Doctor is generally a non-violent pacifist, but Jon Pertwee's Doctor was not afraid to throw down, as shown in this compilation video by another Whovian.
Pertwee left the series in 1974, succeeded by Tom Baker as the Fourth Doctor. (The one with the scarf that no one in my neighborhood had ever heard of.)