The Collaborative International Dictionary of English v.0.48:

Domain \Do*main"\, n. [F. domaine, OF. demaine, L. dominium,
   property, right of ownership, fr. dominus master, owner. See
   Dame, and cf Demesne, Dungeon.]
   1. Dominion; empire; authority.
      [1913 Webster]

   2. The territory over which dominion or authority is exerted;
      the possessions of a sovereign or commonwealth, or the
      like. Also used figuratively. [WordNet sense 2]
      [1913 Webster]

            The domain of authentic history.      --E. Everett.
      [1913 Webster]

            The domain over which the poetic spirit ranges. --J.
                                                  C. Shairp.
      [1913 Webster]

   3. Landed property; estate; especially, the land about the
      mansion house of a lord, and in his immediate occupancy;
      demesne. [WordNet sense 2] --Shenstone.
      [1913 Webster]

   4. (Law) Ownership of land; an estate or patrimony which one
      has in his own right; absolute proprietorship; paramount
      or sovereign ownership.
      [1913 Webster]

   5. (Math.) the set of values which the independent variable
      of a function may take. Contrasted to range, which is
      the set of values taken by the dependent variable.
      [WordNet sense 3]
      [PJC]

   6. (Math.) a connected set of points, also called a region.
      [PJC]

   7. (Physics) a region within a ferromagnetic material,
      composed of a number of atoms whose magnetic poles are
      pointed in the same direction, and which may move together
      in a coordinated manner when disturbed, as by heating. The
      direction of polarity of adjacent domains may be
      different, but may be aligned by a strong external
      magnetic field.
      [PJC]

   8. (Computers) an address within the internet computer
      network, which may be a single computer, a network of
      computers, or one of a number of accounts on a multiuser
      computer. The domain specifies the location (host
      computer) to which communications on the internet are
      directed. Each domain has a corresponding 32-bit number
      usually represented by four numbers separated by periods,
      as 128.32.282.56. Each domain may also have an
      alphabetical name, usually composed of a name plus an
      extension separated by a period, as worldsoul.org; the
      alphabetical name is referred to as a domain name.
      [PJC]

   9. (Immunology) the three-dimensional structure within an
      immunoglobulin which is formed by one of the homology
      regions of a heavy or light chain. --Dict. Sci. Tech.
      [PJC]

   10. the field of knowledge, expertise, or interest of a
       person; as, he had a limited domain of discourse; I can't
       comment on that, it's outside my domain. [WordNet sense
       5]

   Syn: domain, realm, field, area. [PJC]

   11. a particular environment or walk of life. [WordNet sense
       1]

   Syn: sphere, domain, area, orbit, field, arena. [PJC]

   12. people in general; especially a distinctive group of
       people with some shared interest. [WordNet sense 4]

   Syn: world, domain. [PJC]

   Public domain,

   1. the territory belonging to a State or to the general
      government; public lands. [U.S.]

   2. the situation or status of intellectual property which is
      not protected by copyright, patent or other restriction on
      use. Anything

   in the public domain may be used by anyone without
      restriction. The effective term of force of copyrights and
      patents are limited by statute, and after the term
      expires, the writings and inventions thus protected go
      into the public domain and are free for use by all.

   Right of eminent domain, that superior dominion of the
      sovereign power over all the property within the state,
      including that previously granted by itself, which
      authorizes it to appropriate any part thereof to a
      necessary public use, reasonable compensation being made.
      [1913 Webster]

WordNet (r) 3.0 (2006):

public domain
    n 1: property rights that are held by the public at large

The Free On-line Dictionary of Computing (30 December 2018):

public domain
PD
public domain software

   (PD) The total absence of copyright protection.  If
   something is "in the public domain" then anyone can copy it or
   use it in any way they wish.  The author has none of the
   exclusive rights which apply to a copyright work.

   The phrase "public domain" is often used incorrectly to refer
   to freeware or shareware (software which is copyrighted
   but is distributed without (advance) payment).  Public domain
   means no copyright -- no exclusive rights.  In fact the phrase
   "public domain" has no legal status at all in the UK.

   See also archive site, careware, charityware,
   copyleft, crippleware, guiltware, postcardware and
   -ware.  Compare payware.