The Collaborative International Dictionary of English v.0.48:

Approving \Ap*prov"ing\, a.
   Expressing approbation; commending; as, an approving smile.
   -- Ap*prov"ing*ly, adv.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Approve \Ap*prove"\, v. t. [imp. & p. p. Approved; p. pr. &
   vb. n. Approving.] [OE. aproven, appreven, to prove, OF.
   aprover, F. approuver, to approve, fr. L. approbare; ad +
   probare to esteem as good, approve, prove. See Prove, and
   cf. Approbate.]
   1. To show to be real or true; to prove. [Obs.]
      [1913 Webster]

            Wouldst thou approve thy constancy? Approve
            First thy obedience.                  --Milton.
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   2. To make proof of; to demonstrate; to prove or show
      practically.
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            Opportunities to approve . . . worth. --Emerson.
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            He had approved himself a great warrior. --Macaulay.
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            'T is an old lesson; Time approves it true. --Byron.
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            His account . . . approves him a man of thought.
                                                  --Parkman.
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   3. To sanction officially; to ratify; to confirm; as, to
      approve the decision of a court-martial.
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   4. To regard as good; to commend; to be pleased with; to
      think well of; as, we approve the measured of the
      administration.
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   5. To make or show to be worthy of approbation or acceptance.
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            The first care and concern must be to approve
            himself to God.                       --Rogers.
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   Note: This word, when it signifies to be pleased with, to
         think favorably (of), is often followed by of.
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               They had not approved of the deposition of James.
                                                  --Macaulay.
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               They approved of the political institutions. --W.
                                                  Black.
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WordNet (r) 3.0 (2006):

approving
    adj 1: expressing or manifesting praise or approval;
           "approbative criticism"; "an affirmative nod" [syn:
           approving, affirmative, approbative, approbatory,
           plausive]
    n 1: the formal act of approving; "he gave the project his
         blessing"; "his decision merited the approval of any
         sensible person" [syn: blessing, approval, approving]
         [ant: disapproval]