The Collaborative International Dictionary of English v.0.48:

Finesse \Fi`nesse"\ (? or ?), n. [F., fr. fin fine. See Fine,
   a.]
   1. Subtilty of contrivance to gain a point; artifice;
      stratagem.
      [1913 Webster]

            This is the artificialest piece of finesse to
            persuade men into slavery.            --Milton.
      [1913 Webster]

   2. (Whist Playing) The act of finessing. See Finesse, v.
      i., 2.
      [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Finesse \Fi*nesse"\, v. i. [imp. & p. p. Finessed; p. pr. &
   vb. n. Finessing.]
   1. To use artifice or stratagem. --Goldsmith.
      [1913 Webster]

   2. (Whist Playing) To attempt, when second or third player,
      to make a lower card answer the purpose of a higher, when
      an intermediate card is out, risking the chance of its
      being held by the opponent yet to play.
      [1913 Webster]

WordNet (r) 3.0 (2006):

finesse
    n 1: subtly skillful handling of a situation [syn: delicacy,
         diplomacy, discreetness, finesse]