Source : Webster's Revised Unabridged Dictionary (1913)

Edge \Edge\, v. t. [imp. & p. p. {Edged}; p. pr. & vb. n.
   {Edging}.]
   1. To furnish with an edge as a tool or weapon; to sharpen.

            To edge her champion's sword.         --Dryden.

   2. To shape or dress the edge of, as with a tool.

   3. To furnish with a fringe or border; as, to edge a dress;
      to edge a garden with box.

            Hills whose tops were edged with groves. --Pope.

   4. To make sharp or keen, figuratively; to incite; to
      exasperate; to goad; to urge or egg on. [Obs.]

            By such reasonings, the simple were blinded, and the
            malicious edged.                      --Hayward.

   5. To move by little and little or cautiously, as by pressing
      forward edgewise; as, edging their chairs forwards.
      --Locke.

Edging \Edg"ing\, n.
   1. That which forms an edge or border, as the fringe,
      trimming, etc., of a garment, or a border in a garden.
      --Dryden.

   2. The operation of shaping or dressing the edge of anything,
      as of a piece of metal.

   {Edging machine}, a machine tool with a revolving cutter, for
      dressing edges, as of boards, or metal plates, to a
      pattern or templet.

Source : WordNet®

edging
     n : border consisting of anything placed on the edge to finish
         something (such as a fringe on clothing or on a rug)