As I understand it, they give any plane upon which the president is riding the radio code "Air Force One." That way, other crews will understand the need for priority should an emergency arise. Thus, if the Presdent was for some reason flying on Pan Am flight 800, and an emergency arose, everyone would understand the priority needs if the pilot radioed in as "Air Force One" rather than "Pan Am 800." It brings that plane to the top of the list.

In other words, as Ross put it, it's not a designation of a particular peice of vacant aircraft (although im popular culture and the media it often is used to designate the president's designated reserved aircraft). Rather, the phrase "Air Force One" has significant and practical meaning to air and emergency personnel worldwide.