It is explained in The Night Of The Doctor, which is a mini episode prequel to The Day Of The Doctor.
|The 8th Doctor Dead, Before The Sisterhood Resurrect Him|
The Doctor crash lands on Karn, where the Sisterhood of Karn brings him back to life and give him an elixir to turn him into a warrior, or The War Doctor. In that episode it also says they can give him an elixir to choose to be a man or woman. (I personally think that is how The Master became Missy.)
|The War Doctor Regeneration|
During The War Doctor's regeneration you sort of see a resemblance in the eyes and chin of Christopher Eccleston, The Ninth Doctor, Eccleston, didn't actually participate in filming of the 50th Anniversary episode. Above is where they cut away in the episode and below is from the extended take, which was cut. Moffat said is was to respect Eccleston's wishes not to participate and so it wouldn't make people think that he took part in filming. The part where you see him at the end with all the other doctors was edited from stock footage.
|The War Doctor Regeneration, Extended Clip|
Below is a Doctor Who: The Doctors, Then And Now video.