One could define the administrative department by saying that it includes everything that is not part of the other departments, but one can define it in a more positive manner by saying that it is specifically responsible for

ensuring that unity of action, discipline, anticipation, activity, order, etc., exist in all parts of the enterprise | recruiting, organizing and directing the workforce | ensuring good relations between the various departments and with the outside world | coordination of all efforts towards the overall goal | satisfying shareholders and employees; labor and management.