The Collaborative International Dictionary of English v.0.48:

Execute \Ex"e*cute\, v. t. [imp. & p. p. Executed; p. pr. &
   vb. n. Executing.] [F. ex['e]cuter, L. executus, exsecutus,
   p. p. of exequi to follow to the end, pursue; ex out + sequi
   to follow. See Second, Sue to follow up, and cf.
   Exequy.]
   1. To follow out or through to the end; to carry out into
      complete effect; to complete; to finish; to effect; to
      perform.
      [1913 Webster]

            Why delays
            His hand to execute what his decree
            Fixed on this day?                    --Milton.
      [1913 Webster]

   2. To complete, as a legal instrument; to perform what is
      required to give validity to, as by signing and perhaps
      sealing and delivering; as, to execute a deed, lease,
      mortgage, will, etc.
      [1913 Webster]

   3. To give effect to; to do what is provided or required by;
      to perform the requirements or stipulations of; as, to
      execute a decree, judgment, writ, or process.
      [1913 Webster]

   4. To infect capital punishment on; to put to death in
      conformity to a legal sentence; as, to execute a traitor.
      [1913 Webster]

   5. To put to death illegally; to kill. [Obs.] --Shak.
      [1913 Webster]

   6. (Mus.) To perform, as a piece of music or other feat of
      skill, whether on an instrument or with the voice, or in
      any other manner requiring physical activity; as, to
      execute a difficult part brilliantly; to execute a coup;
      to execute a double play.

   Syn: To accomplish; effect; fulfill; achieve; consummate;
        finish; complete. See Accomplish.
        [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

executing \ex"e*cut`ing\ n.
   putting a condemned person to death.

   Syn: execution, capital punishment, death penalty.
        [WordNet 1.5]

WordNet (r) 3.0 (2006):

executing
    n 1: putting a condemned person to death [syn: execution,
         executing, capital punishment, death penalty]