Source : Webster's Revised Unabridged Dictionary (1913)

Compliment \Com"pli*ment\, n. [F. compliment. It complimento,
   fr. comlire to compliment, finish, suit, fr. L. complere to
   fill up. See {Complete}, and cf. {Complement}.]
   An expression, by word or act, of approbation, regard,
   confidence, civility, or admiration; a flattering speech or
   attention; a ceremonious greeting; as, to send one's
   compliments to a friend.

         Tedious waste of time, to sit and hear So many hollow
         compliments and lies.                    --Milton.

         Many a compliment politely penned.       --Cowper.

   {To make one a compliment}, to show one respect; to praise
      one in a flattering way. --Locke.

   {To make one's compliments to}, to offer formal courtesies
      to.

   {To stand on compliment}, to treat with ceremony.

   Syn: See {Adulation}.

Compliment \Com"pli*ment\, v. t.
   To praise, flatter, or gratify, by expressions of
   approbation, respect, or congratulation; to make or pay a
   compliment to.

         Monarchs should their inward soul disguise; . . .
         Should compliment their foes and shun their friends.
                                                  --Prior.

   Syn: To praise; flatter; adulate; commend.

Compliment \Com"pli*ment\, v. i.
   To pass compliments; to use conventional expressions of
   respect.

         I make the interlocutors, upon occasion, compliment
         with one another.                        --Boyle.

Source : WordNet®

compliment
     n : a remark (or act) expressing praise and admiration

compliment
     v 1: say something to someone that expresses praise; "He
          complimented her on her last physics paper" [syn: {congratulate}]
     2: express respect or esteem for