The Collaborative International Dictionary of English v.0.48:

Copier \Cop"i*er\, n. [From. Copy.]
   1. One who copies; one who writes or transcribes from an
      original; a transcriber.
      [1913 Webster]

   2. An imitator; one who imitates an example; hence, a
      plagiarist.
      [1913 Webster]

   3. a machine that makes copies of documents, especially by
      xerography; a photocopier; as, to run twenty copies off on
      the copier.
      [PJC]

WordNet (r) 3.0 (2006):

copier
    n 1: apparatus that makes copies of typed, written or drawn
         material [syn: duplicator, copier]