Doctor Who first appeared on British TV in 1963 (which happens to be the year I was born) and continued until 1989. There was an unsuccessful attempt to revive the series for the American market, but the real revival didn't come until 2005, when the BBC broadcast the first season of a new series with Christopher Eccleston playing the Doctor.
Over the years the Doctor has been played by different actors, and there have been different producers and different script editors working on the show. With each significant change in cast and crew the tone of the programme, and even the genre it was in, changed. The programme also reflects the major changes in television technology and storytelling that have taken place over the years.
'Classic' Doctor Who comes in self-contained serials that usually consist of four or six episodes of 25 minutes each. New Doctor Who has stand-alone episodes (though there have been some multi-parters) of 50 minutes each.
You don't really need to know a lot of back-story to understand what's going on, though you may enjoy the programme more if you do. The Doctor is an alien, a so-called Time Lord, from a planet called Gallifrey. The Doctor travels through space and time in the Tardis, a vessel looking from the outside like a 1950's police box, with one or more companions. The first companion was the Doctor's granddaughter, and her successors were humans and aliens who the Doctor picked up along the way. Usually, knowing their back-stories does little to actually explain their presence. The Doctor doesn't die but instead he regenerates into a new body with a new personality (and a new actor playing the part).
Some time in the summer of 2006 I became something of a Doctor Who fan and found myself buying quite a lot of Doctor Who DVDs. At the time I was also trying to get back into the habit of writing again, and reviewing Doctor Who made a nice break from my usual subject matter. I discovered that reviews were fun to write, and surprisingly hard to write well.
I'm planning to write reviews of all 'classic' Doctor Who serials and new series episodes that come out on DVD.