The Collaborative International Dictionary of English v.0.48:

Extermination \Ex*ter`mi*na"tion\, n. [Cf. F. extermination.]
   1. The act of exterminating; total destruction; eradication;
      excision; as, the extermination of inhabitants or tribes,
      of error or vice, or of weeds from a field.
      [1913 Webster]

   2. (Math.) Elimination. [R.]
      [1913 Webster]

WordNet (r) 3.0 (2006):

extermination
    n 1: complete annihilation; "they think a meteor cause the
         extinction of the dinosaurs" [syn: extinction,
         extermination]
    2: the act of exterminating [syn: extermination,
       liquidation]