A hierarchy is a system of ranking and organizing things or people such that each element (except for the top element) is a subordinate to a single other element. A hierarchy can be an ordered list, a tree structure, or a combination of these.
Social hierarchies are hierarchies in which the elements are people. Commonly, seniors in the apex position have more power than their subordinates. Thus, the asymmetrical relationship might be one "has power over" others. This power can involve the authority and the right to make rules, to make decisions, to give the subordinate(s) orders, and possibly to reward and to punish them according to their behavior and performance.
Examples of institutions with clear (and often formal) social hierarchies among their members: