The Collaborative International Dictionary of English v.0.48:

Packing \Pack"ing\, n.
   1. The act or process of one who packs.
      [1913 Webster]

   2. Any material used to pack, fill up, or make close.
      Specifically (Mach.): A substance or piece used to make a
      joint impervious; as:
      (a) A thin layer, or sheet, of yielding or elastic
          material inserted between the surfaces of a flange
          joint.
      (b) The substance in a stuffing box, through which a
          piston rod slides.
      (c) A yielding ring, as of metal, which surrounds a piston
          and maintains a tight fit, as inside a cylinder, etc.
          [1913 Webster]

   3. (Masonry) Same as Filling. [Rare in the U. S.]
      [1913 Webster]

   4. A trick; collusion. [Obs.] --Bale.
      [1913 Webster]

   Cherd packing (Bridge Building), the arrangement, side by
      side, of several parts, as bars, diagonals, a post, etc.,
      on a pin at the bottom of a chord. --Waddell.

   Packing box, a stuffing box. See under Stuffing.

   Packing press, a powerful press for baling cotton, wool,
      hay, etc.

   Packing ring. See Packing, 2
      (c), and Illust. of Piston.

   Packing sheet.
      (a) A large cloth for packing goods.
      (b) A sheet prepared for packing hydropathic patients.
          [1913 Webster]

WordNet (r) 3.0 (2006):

packing box
    n 1: a small chamber in which packing is compressed around a
         reciprocating shaft or piston to form a seal [syn:
         stuffing box, packing box]
    2: a large crate in which goods are packed for shipment or
       storage [syn: packing box, packing case]