The Doctor is the main character in Doctor Who. He is an alien called a Time Lord, in fact, the last of the time lords. He travels around in his time machine called the TARDIS (time and relative dimension in space) and continually battles aliens and saves earth.
The Time war
There was a war between the Daleks and the Time Lords, the Doctor fought on the front lines, and in order to stop the war, he blew up both the Daleks and the Time Lords along with their home planet, Gallifrey.
These are the Daleks, somehow a few escaped the time war, so the Doctor is locked in eternal combat with them.
Time Lords can escape death by regenerating, as in completely changing their appearance, (aka. a new actor comes in and replaces the old one, that's how the show has been going on for 50 years.) The Doctor is on his 11th regeneration.
The Doctor almost always travels with a companion, and it's usually a woman, and they usually have a tragic ending, they need to, because other wise they would want to travel with the Doctor forever.
The Master is the only other time lord besides the Doctor, but he's usually thought to be dead, the Master is slightly insane and has been in DW since the beginning.
A whovian is someone who is a fan of Doctor Who, they tend to range from liking the show to slightly obsessed.