The Collaborative International Dictionary of English v.0.48:

Dominion \Do*min"ion\, n. [LL. dominio, equiv. to L. dominium.
   See Domain, Dungeon.]
   1. Sovereign or supreme authority; the power of governing and
      controlling; independent right of possession, use, and
      control; sovereignty; supremacy.
      [1913 Webster]

            I praised and honored him that liveth forever, whose
            dominion is an everlasting dominion.  --Dan. iv. 34.
      [1913 Webster]

            To choose between dominion or slavery. --Jowett
                                                  (Thucyd. ).
      [1913 Webster]

   2. Superior prominence; predominance; ascendency.
      [1913 Webster]

            Objects placed foremost ought . . . have dominion
            over things confused and transient.   --Dryden.
      [1913 Webster]

   3. That which is governed; territory over which authority is
      exercised; the tract, district, or county, considered as
      subject; as, the dominions of a king. Also used
      figuratively; as, the dominion of the passions.
      [1913 Webster]

   4. pl. A supposed high order of angels; dominations. See
      Domination, 3. --Milton.
      [1913 Webster]

            By him were all things created . . . whether they be
            thrones, or dominions, or principalities, or powers.
                                                  --Col. i. 16.

   Syn: Sovereignty; control; rule; authority; jurisdiction;
        government; territory; district; region.
        [1913 Webster]

WordNet (r) 3.0 (2006):

dominion
    n 1: dominance or power through legal authority; "France held
         undisputed dominion over vast areas of Africa"; "the rule
         of Caesar" [syn: dominion, rule]
    2: a region marked off for administrative or other purposes
       [syn: district, territory, territorial dominion,
       dominion]
    3: one of the self-governing nations in the British Commonwealth

Moby Thesaurus II by Grady Ward, 1.0:

189 Moby Thesaurus words for "dominion":
   acme, administration, ally, ambit, antecedence, antecedency,
   anteposition, anteriority, archduchy, archdukedom, area, arena,
   ascendance, ascendancy, ascendant, authority, authorization,
   bailiwick, balance of power, be-all and end-all, beat, blue ribbon,
   body politic, border, borderland, buffer state, captive nation,
   champaign, championship, chieftaincy, chieftainry, circle, circuit,
   city-state, claws, clutches, colony, command, commonweal,
   commonwealth, control, country, county, demesne, department,
   directorship, disposition, domain, dominance, dominancy,
   domination, dominium, duchy, dukedom, earldom, effectiveness,
   eminent domain, empery, empire, field, first place, first prize,
   free city, front position, governance, government, grand duchy,
   grasp, grip, gripe, hand, hands, headship, hegemony, height, helm,
   hemisphere, highest, hold, imperium, influence, iron hand,
   judicial circuit, jurisdiction, kingdom, kingship, land,
   land tenure, landholding, landownership, landowning, leadership,
   lordship, management, mandant, mandate, mandated territory,
   mandatee, mandatory, march, masterdom, mastership, mastery,
   maximum, most, nation, nationality, ne plus ultra, new high, orb,
   orbit, overlordship, ownership, pale, palms, paramountcy, polis,
   polity, possession, possessorship, power, precedence, precedency,
   preceding, precession, precinct, precursor, predominance,
   predominancy, predomination, preeminence, preference, prefixation,
   prelude, preponderance, prepotence, prepotency, presidency,
   primacy, principality, principate, priority, property, proprietary,
   proprietorship, protectorate, prothesis, province,
   puppet government, puppet regime, raj, realm, record, region,
   regnancy, reign, reins of government, republic, round, rule,
   satellite, say, seigniory, seneschalty, settlement,
   sovereign nation, sovereignty, sphere, state, sultanate,
   superiority, superpower, supremacy, suzerainship, suzerainty, sway,
   talons, terrain, territory, the lead, top priority, top spot,
   toparchia, toparchy, upper hand, urgency, walk, whip hand,
   zenith