The Collaborative International Dictionary of English v.0.48:

anaphora \a*naph"o*ra\ ([.a]*n[a^]f"[-o]*r[.a]), n. [L., fr. Gr.
   'anafora`, fr. 'anafe`rein to carry up or back; 'ana` +
   fe`rein to carry.] (Rhet.)
   1. A repetition of a word or of words at the beginning of two
      or more successive clauses.
      [1913 Webster]

   2. The use of a substitute word, such as a pronoun, in
      reference to a something already mentioned in a discourse;
      also, the relation between the substitute word and its
      antecedent. It is contrasted with cataphora, the use of
      a pronoun for a word or topic not yet mentioned.

   Note: Thus, in the sentence "John was tall but he was not
         very heavy." the "he" is an anaphora for John, or an
         anaphoric reference to John.
         [PJC]

WordNet (r) 3.0 (2006):

anaphora
    n 1: using a pronoun or similar word instead of repeating a word
         used earlier
    2: repetition of a word or phrase at the beginning of successive
       clauses [syn: epanaphora, anaphora]