Source : Webster's Revised Unabridged Dictionary (1913)

Quartter \Quart"ter\, v. t. [imp. & p. p. {Quartered}; p. pr. &
   vb. n. {Quartering}.]
   1. To divide into four equal parts.

Quartering \Quar"ter*ing\, a.
   1. (Naut.) Coming from a point well abaft the beam, but not
      directly astern; -- said of waves or any moving object.

   2. (Mach.) At right angles, as the cranks of a locomotive,
      which are in planes forming a right angle with each other.

Quartering \Quar"ter*ing\, n.
   1. A station. [Obs.] --Bp. Montagu.

   2. Assignment of quarters for soldiers; quarters.

   3. (Her.)
      (a) The division of a shield containing different coats of
          arms into four or more compartments.
      (b) One of the different coats of arms arranged upon an
          escutcheon, denoting the descent of the bearer.

   4. (Arch.) A series of quarters, or small upright posts. See
      {Quarter}, n., 1
      (m) (Arch.) --Gwilt.

   {Quartering block}, a block on which the body of a condemned
      criminal was quartered. --Macaulay.

Source : WordNet®

quartering
     n 1: a coat of arms that occupies one quarter of an escutcheon;
          combining four coats of arms on one shield usually
          represented intermarriages
     2: living accommodations (especially those assigned to military
        personnel)
     3: dividing into four equal parts