The First Lady of the United States is the chief hostess of the White House. It is her duty to meet and greet foreign dignitaries, domestic politicians, or others who request the President's time. She also serves as chief party planner for any events that take place within the White House. Contrary to popular belief, she is not officially the President's wife, though in practice she almost always is. In the event the President does not have a wife while in office, the job is usually taken by a close female relative of his, such as a mother or sister.
Though lacking in the way of official power, most modern First Ladies have taken on some domestic policy issue as part of a general "campaign" of theirs, usually something non-political in nature such as city beautification (Ladybird Johnson), health (Nancy Reagan, Hillary Clinton), education (Laura Bush), or public service (Michelle Obama). Though not explicitly stated within the context of the show, Abigail Bartlet's domestic campaign was likely public health, based on her previous profession as a physician.