The Collaborative International Dictionary of English v.0.48:

brierwood \bri"er*wood`\ n.
   1. wood from the hard woody root of the briar Erica
      arborea; it is used to make tobacco pipes. See also 2nd
      brier and brier root.

   Syn: briarwood.
        [WordNet 1.5]

WordNet (r) 3.0 (2006):

brier-wood
    n 1: wood from the hard woody root of the briar Erica arborea;
         used to make tobacco pipes [syn: briarwood, brierwood,
         brier-wood]