Air Force One was the official plane the President used when making official trips.
In the film, Air Force One was the plane that many U.S government officials (ironically, minus the President himself as he chooses to stay behind with his wife and his people but his daughter didn't stay behind) used to fly from Washington D.C. to China when the world apocalypse happened. They fly, luckily avoiding the ash cloud that's 'swallowing' the United States just a few hours before it. Inside the airplane, many staffs of the U.S government collected updates information around the world concerning the 2012 apocalypse.
It is later caught by a mega-tsunami just one minute left before the mega-tsunami hit the arks, then it was destroyed when collided into Ark 4.