The Collaborative International Dictionary of English v.0.48:

Hierarchy \Hi"er*arch`y\ (h[imac]"[~e]r*[aum]rk`[y^]), n.; pl.
   Hierarchies (h[imac]"[~e]r*[aum]rk`[i^]z). [Gr.
   'ierarchi`a: cf. F. hi['e]rarchie.]
   1. Dominion or authority in sacred things.
      [1913 Webster]

   2. A body of officials disposed organically in ranks and
      orders each subordinate to the one above it; a body of
      ecclesiastical rulers.
      [1913 Webster]

   3. A form of government administered in the church by
      patriarchs, metropolitans, archbishops, bishops, and, in
      an inferior degree, by priests. --Shipley.
      [1913 Webster]

   4. A rank or order of holy beings.
      [1913 Webster]

            Standards and gonfalons . . . for distinction serve
            Of hierarchies, of orders, and degrees. --Milton.

   5. (Math., Logic, Computers) Any group of objects ranked so
      that every one but the topmost is subordinate to a
      specified one above it; also, the entire set of ordering
      relations between such objects. The ordering relation
      between each object and the one above is called a
      hierarchical relation.

   Note: Classification schemes, as in biology, usually form
         hierarchies.
         [PJC]

WordNet (r) 3.0 (2006):

hierarchy
    n 1: a series of ordered groupings of people or things within a
         system; "put honesty first in her hierarchy of values"
    2: the organization of people at different ranks in an
       administrative body [syn: hierarchy, power structure,
       pecking order]

The Free On-line Dictionary of Computing (19 January 2023):

hierarchy

   An organisation with few things, or one thing, at the top and
   with several things below each other thing.  An inverted tree
   structure.  Examples in computing include a directory
   hierarchy where each directory may contain files or other
   directories; a hierarchical network (see hierarchical
   routing), a class hierarchy in object-oriented
   programming.

   (1994-10-11)