The Collaborative International Dictionary of English v.0.48:

Precinct \Pre"cinct\ (?; 277), n. [LL. praecinctum, fr. L.
   praecingere, praecinctum, to gird about, to encompass; prae
   before + cingere to gird, surround. See Pre-, and
   Cincture.]
   1. The limit or exterior line encompassing a place; a
      boundary; a confine; limit of jurisdiction or authority;
      -- often in the plural; as, the precincts of a state. "The
      precincts of light." --Milton.
      [1913 Webster]

   2. A district within certain boundaries; a minor territorial
      or jurisdictional division; as, an election precinct; a
      school precinct.
      [1913 Webster]

   3. A parish or prescribed territory attached to a church, and
      taxed for its support. [U.S.]
      [1913 Webster]

            The parish, or precinct, shall proceed to a new
            choice.                               --Laws of
                                                  Massachusetts.
      [1913 Webster]

WordNet (r) 3.0 (2006):

precinct
    n 1: a district of a city or town marked out for administrative
         purposes

Moby Thesaurus II by Grady Ward, 1.0:

161 Moby Thesaurus words for "precinct":
   Kreis, agora, ambit, amphitheater, approach, approximation,
   archbishopric, archdiocese, area, arena, arrondissement,
   athletic field, auditorium, background, bailiwick, bear garden,
   beat, bishopric, border, borderland, borders, borough, boundary,
   bounds, bowl, boxing ring, bull ring, campus, canton, canvas,
   champaign, circle, circuit, circus, city, close borough, closeness,
   cockpit, coliseum, colosseum, commune, compass, confines,
   congressional district, constablewick, convergence, county, course,
   demesne, departement, department, diocese, district, domain,
   dominion, duchy, election district, electoral district, electorate,
   environs, field, floor, foreground, forum, gerrymander,
   gerrymandered district, government, ground, gym, gymnasium, hall,
   hamlet, hemisphere, hippodrome, hundred, immediacy,
   immediate foreground, judicial circuit, jurisdiction, limits,
   lists, locale, magistracy, march, marketplace, mat, metropolis,
   metropolitan area, milieu, nearness, neighborhood, nighness,
   oblast, okrug, open forum, orb, orbit, palaestra, pale,
   parade ground, parish, pit, place, platform, pocket borough,
   precincts, principality, prize ring, propinquity, province,
   proximity, public square, purlieu, purlieus, quarter, range, realm,
   region, riding, ring, rotten borough, round, safe district, scene,
   scene of action, scenery, section, sector, setting, sheriffalty,
   sheriffwick, shire, shrievalty, silk-stocking district,
   single-member district, site, soke, sphere, squared circle,
   stadium, stage, stage set, stage setting, stake, state,
   swing district, terrain, territory, theater, tilting ground,
   tiltyard, town, township, vicinage, vicinity, village, walk,
   wapentake, ward, wrestling ring, zone



Bouvier's Law Dictionary, Revised 6th Ed (1856):

PRECINCT. The district for which a high or petty constable is appointed, is
in England, called a precinct. Willc. Office of Const. xii.
     2. In day time all persons are bound to recognize a constable acting
within his own precincts; after night the constable is required to make
himself known, and it is, indeed, proper he should do so at all times. Ibid.
n. 265, p. 93.