SPOILERS!
The Eleventh Doctor, as portrayed by Matt Smith, is the 11th incarnation of The Doctor, the eponymous time travelling alien of the long running British Broadcasting Company science-fiction adventure/drama Doctor Who. The Eleventh Doctor has so far featured in two series of Doctor Who, and is expected to do a third and possibly a fourth before passing on the role.
A bit has to be said about Doctor Who, The Doctor, and the classic and revival versions of the show before we can move on to the Eleventh Doctor, proper. Doctor Who is a show that is both camp and avante-garde, with the very open premise that The Doctor shows up via his time machine in a random location and rights wrongs and helps people, usually through a mixture of wits, compassion and bravery. Since he can travel through all of time and space, a story can be an Edwardian costume drama or a reality-bending space opera. The show ran for 27 years on the BBC, was cancelled, and was relaunched in 2005, with much higher production values.
The Doctor, as a character, is an enigma, being a mixture of earthy humanity with cosmic wisdom, and a mixture of otherworldly coldness with strident morality. When he "dies", he regenerates, leading to a new actor to take the role, communicating the same basic personality, through a different persona. The Doctor's basic values and memories don't change, but his mannerisms and attitude vary widely.
When the show was relaunched in 2005, there were some doubts if a confusing, camp and sometimes shoddily-done show could capture a new audience. That it succeeded was due in large parts to the efforts of Christopher Eccleston as The Ninth Doctor, and of David Tennant's iconic portrayal of The Tenth Doctor. Both of these actors were young, putting some verve and energy into a role that had sometimes been stodgy. David Tennant's charming nature also is part of the reason why much of revival Who's fanbase is female.
All of which caused some concern when Matt Smith was announced as the successor of Tennant. For one thing, he was the youngest actor to play the role. Could a 28 year old man play the role of a 900+ year old alien? And could anyone replace the warm charm of David Tennant?
Although there are some dissenters, much of the fanbase, myself included, think that Smith redefined the role as his own in the first episode he was in, and has continued to expand on it since then.
The angle that Smith has taken to the role is a fairly obvious one, although the skill to carry it out is his alone. While Tennant infused the role with warm charm (mixed with some anger), Smith has portrayed The Doctor as an alien. Which makes sense: The Doctor is a Time Lord, the last of a species of alien that were the most powerful beings in the universe for aeons. Although he looks human, and has a warm personality, he is still an alien. Smith communicates this by portraying the Eleventh Doctor as ticky, manic and a bit confused about the way other people perceive the world. He is the most physical actor to play the role, with his hand gestures and habit of spinning around in weird directions making him amusing to watch.
"Is this the way time normally happens? So slowly, and all in the right order?"
Interestingly enough, despite concerns about such a young actor playing the role, The Eleventh Doctor acts very old. His distinctive accessory is a bowtie, which he cluelessly defends with the phrase "Bowties are cool". He acts like an old, absent minded professor. He is more cerebral and nerdy than his two earlier incarnations.
On the other hand, and this is why the role of The Doctor can be fascinating despite its camp origins, he is also one of the more militant incarnations of The Doctor. He has had some great one-liners and boasts, and he seems to move with more foresight and manipulation than The Tenth Doctor did. While personally as goofy and silly as ever, some of the plots he has hatched against his enemies have been truly fearsome.
"Good men don't need rules. Today is not the day for you to find out why I have so many."
Despite his alien nature, the Eleventh Doctor has had the most constant companions of any new series Doctor. In fact, in The Wedding of River Song, he even gets married! His companions are Amy Pond and Rory Williams, a couple who get married during the show. It later turns out (in one of Doctor Who's most famous and convoluted plotlines) that their daughter turns out to be River Song, whose conception in the TARDIS led to her being a partial Time Lady. Thus, one of the most lonely and alien of The Doctor's incarnations is also the one who ends up travelling with a wife, a mother-in-law, and a father-in-law.
Next to Matt Smith's portrayal, a big part of what has made the Eleventh Doctor distinctive is that the head writer of the program has been Steven Moffat, who has changed the tone and focus of the program. While stories in the Russel T Davies era tended to be camp, silly and accessible to the average viewer, Moffat's plots have been timey-wimey, involving intricate and reality-bending conspiracies and complicated character backgrounds.
For now, the Eleventh Doctor is considered to be a solid addition to Doctor Who's legacy, although it is still unclear whether he will become quite as iconic for the program as David Tennant was. Doctor Who's fanbase doesn't agree on much, and sometimes the value of work changes as the years pass. However, my own guess is that The Eleventh Doctor will be seen as one of the greats.
Internally to the story, much remains to be seen about how both the plot threads and character development of the Doctor ends up. Is he a bumbling fool or a canny mastermind? Is he a gentle pacifist or a ruthless warrior? The dynamic has been set up, and seeing how it will revolve is the best part of the character.