The Collaborative International Dictionary of English v.0.48:

Curler \Curl"er\ (k[^u]rl"[~e]r), n.
   1. One who, or that which, curls.
      [1913 Webster]

   2. A player at the game called curling. --Burns.
      [1913 Webster]

   3. A small cylindrical object sometimes having a clamping
      attachment, around which hair is wound so as to produce
      curls; as, she slept all night with a head full of
      curlers.
      [PJC]

   4. an electrical appliance with a handle and a metal
      rod-shaped tip which is heated and around which hair is
      wound, to produce curls in the hair; -- called also
      curling iron.
      [PJC]

WordNet (r) 3.0 (2006):

curler
    n 1: a mechanical device consisting of a cylindrical tube around
         which the hair is wound to curl it; "a woman with her head
         full of curlers is not a pretty sight" [syn: curler,
         hair curler, roller, crimper]