Here is the chronology of the time war's final events (spoilers if you haven't seen the special, don't scroll down):
-The Doctor steals the Moment and heads to utilize it to end the Time War by burning Gallifrey, destroying Time Lords and Daleks alike.
-A time lock has already been placed upon Gallifrey in order to prevent Time Lords and Daleks from changing history to give themselves the upper hand. Thus, the fighting is inside the lock, and it prevents anyone from getting in or out.
-The High Council of Gallifrey are aware the Doctor has the Moment and believe he is going to use it to destroy everything. Using the Master, the High Council attempt to escape the time lock by inserting the sound of drums within the Master's head, him being their only way out of the time lock (The End of Time events). The 10th Doctor thwarts this and sends the High Council back into the time lock.
-Back to the War Doctor, who is about to use the Moment to burn Gallifrey. The Moment personified as Bad Wolf Rose appears and shows the Doctor what he will become if he destroys Gallifrey. These are the Day of the Doctor events.
-All 13 Doctors come together to send Gallifrey into a pocket universe, frozen in time such as the paintings with the Zygons. The Gallifrey War Room decides to go along with this, as the High Council has failed in their plans.
-Gallifrey is sealed away, still time locked, frozen in a pocket universe. All of the Doctors return to their various timelines.
-The War Doctor and the 10th Doctor, as soon as they leave the presence of the 11th Doctor, forget the events of The Day of the Doctor. The War Doctor, without memories of the events, believes that he DID use the Moment to destroy Gallifrey, as it has disappeared, and thus he, the 9th, and the 10th Doctor's timelines remain the same, them believing that they are the only survivors of the Time War and the guilt of destroying so many races placed upon them, despite the fact that this isn't truly the case. The 11th Doctor believes this as well, up until the events of the Day of the Doctor.
-The 11th Doctor speaks with the Curator and discovers that their plan worked, and that Gallifrey is out there, sealed away. This ties together loose ends such as "how did any of the Daleks escape the Time War?"
So, effectively, all of the Doctor Who timeline stays the same until here on going forward. Now, the Doctor has discovered Gallifrey still exists, the Time Lords still are out there somewhere, and his purpose is now to find his people and return to visit his home world. Some people are complaining that "the Time Lords were so vicious at the end that they were going to destroy the universe, why would the Doctor want to find them?" I personally believe that only the High Council had reached that level of viciousness and that the other citizens (the ones we saw in the Day of the Doctor) were all still good people. So there is a potential antagonist set of Time Lords still out there for the Doctor to face, and I believe after that Gallifrey will be restored to a peaceful, somewhat stuck up planet like it was in the Classic Era. This also allows for the Master's return, as he was sent back with Rassilon and the Time Lords in the End of Time, meaning that he is alive on Gallifrey as well.
Essentially, Moffat has opened up an entire new perspective for the show and has allowed for an abundance of stories with this episode, such as:
-The Doctor setting off to find Gallifrey
-The Doctor and the Master
-The Doctor and the cruel Time Lords
-How the Doctor will get more regenerations given that Capaldi is now effectively the last biologically-allotted incarnation of the Doctor
-How does the Trenzalore mythos get changed in order to allow the Doctor to continue on from his Matt Smith incarnation?
also, Tom Baker as the Curator was the greatest thing ever. I now believe that in his last incarnation, the Doctor regenerates into an old Tom Baker and retires to work in an art museum (also to beekeep.)