Air Force One was the designation given to an aircraft carrying the President of the United States of America. Though specially-modified airplanes are usually used for presidential transport, the designation is applied to any craft the president happens to be on.
In 1972, Gary Seven and Roberta Lincoln boarded Air Force One while President Richard Nixon was en route to Beijing, China. Lincoln was impressed being aboard the plane, though Seven reminded her that, as a child, she and her parents had been on a commercial airliner that President Dwight D. Eisenhower had also been aboard, meaning she had previously been aboard a flight designated Air Force One. (TOS - Star Trek: Assignment: Earth comic: "Too Many Presidents")