The Collaborative International Dictionary of English v.0.48:

Clincher \Clinch"er\, n.
   1. One who, or that which, clinches; that which holds fast.
      --Pope.
      [1913 Webster]

   2. That which ends a dispute or controversy; a decisive
      argument.
      [1913 Webster]

WordNet (r) 3.0 (2006):

clincher
    n 1: an argument that is conclusive [syn: clincher,
         determiner, determining factor]
    2: a point or fact or remark that settles something conclusively
       [syn: clincher, decisive factor]
    3: a tool used to clinch nails or bolts or rivets