Two bases of obeying the authority are following :
Belief is the most important base behind the obedience of the authority. Subordinates obey the orders of their authority because they have faith in him/her. The more deep is this faith in authority, more easy is to obey the orders and for this the authority needs not to use of power.
The uniformity of thoughts and ideals between authority and subordinates is also one of the important reasons behind obedience of authority. Generally people give more importance to suggestions and orders of those who have ideological uniformity with them (subordinates).