What is Hierarchy?

Legal Definition
A hierarchy (from the Greek hierarchia, "rule of a high priest", from hierarkhes, "leader of sacred rites") is an arrangement of items (objects, names, values, categories, etc.) in which the items are represented as being "above," "below," or "at the same level as" one another.

A hierarchy can link entities either directly or indirectly, and either vertically or diagonally. The only direct links in a hierarchy, insofar as they are hierarchical, are to one's immediate superior or to one of one's subordinates, although a system that is largely hierarchical can also incorporate alternative hierarchies. Indirect hierarchical links can extend "vertically" upwards or downwards via multiple links in the same direction, following a path. All parts of the hierarchy which are not linked vertically to one another nevertheless can be "horizontally" linked through a path by traveling up the hierarchy to find a common direct or indirect superior, and then down again. This is akin to two co-workers or colleagues; each reports to a common superior, but they have the same relative amount of authority. Organizational forms exist that are both alternative and complementary to hierarchy. Heterarchy is one such form.

A hierarchy is a system or organization in which people or groups are ranked one above the other according to status or authority.
-- Wikipedia
Legal Definition
Eccl. law. A hierarchy signified, originally, power of the priest; for in the beginning of societies, the priests were entrusted with all the power but, among the priests themselves, there were different degrees of power and authority, at the summit of which was the sovereign pontiff, and this was called the hierarchy. Now it signifies, not so much the power of the priests as the border of power.
-- Bouviers Law Dictionary
Legal Definition
Originally, government by a body of priests. Now, the body of officers in any church or ecclesiastical institution, considered as forming an ascending series of ranks or degrees of power and authority, with the correlative subjection, each to the one next above. Derivatively, any body of men, taken in their public capacity, and considered as forming a chain of powers, as above described.
-- Black's Law Dictionary