The Collaborative International Dictionary of English v.0.48:

Osier \O"sier\, n. [F. osier: cf. Prov. F. oisis, Armor. ozil,
   aozil, Gr. ?, ?, ?, L. vitex, and E. withy.] (Bot.)
      (a) A kind of willow (Salix viminalis) growing in wet
          places in Europe and Asia, and introduced into North
          America. It is considered the best of the willows for
          basket work. The name is sometimes given to any kind
          of willow.
      (b) One of the long, pliable twigs of this plant, or of
          other similar plants.
          [1913 Webster]

                The rank of osiers by the murmuring stream.
                                                  --Shak.
          [1913 Webster]

   Osier bed, or Osier holt, a place where willows are grown
      for basket making. [Eng.]

   Red osier.
      (a) A kind of willow with reddish twigs (Salix rubra).
      (b) An American shrub (Cornus stolonifera) which has
          slender red branches; -- also called osier cornel.
          [1913 Webster]

WordNet (r) 3.0 (2006):

red osier
    n 1: common North American shrub with reddish purple twigs and
         white flowers [syn: red osier, red osier dogwood, red
         dogwood, American dogwood, redbrush, Cornus
         stolonifera]
    2: Eurasian osier having reddish or purple twigs and bark rich
       in tannin [syn: purple willow, red willow, red osier,
       basket willow, purple osier, Salix purpurea]