The Collaborative International Dictionary of English v.0.48:

Elegance \El"e*gance\, Elegancy \El"e*gan*cy\, n. [L. elegantia,
   fr. elegans, -antis, elegant: cf. F. ['e]l['e]gance.]
   1. The state or quality of being elegant; beauty as resulting
      from choice qualities and the complete absence of what
      deforms or impresses unpleasantly; grace given by art or
      practice; fine polish; refinement; -- said of manners,
      language, style, form, architecture, etc.
      [1913 Webster]

            That grace that elegance affords.     --Drayton.
      [1913 Webster]

            The endearing elegance of female friendship.
                                                  --Johnson.
      [1913 Webster]

            A trait of native elegance, seldom seen in the
            masculine character after childhood or early youth,
            was shown in the General's fondness for the sight
            and fragrance of flowers.             --Hawthorne.
      [1913 Webster]

   2. That which is elegant; that which is tasteful and highly
      attractive.
      [1913 Webster]

            The beautiful wildness of nature, without the nicer
            elegancies of art.                    --Spectator.

   Syn: Elegance, Grace. Elegance implies something of a
        select style of beauty, which is usually produced by
        art, skill, or training; as, elegance of manners,
        composition, handwriting, etc.; elegant furniture; an
        elegant house, etc. Grace, as the word is here used,
        refers to bodily movements, and is a lower order of
        beauty. It may be a natural gift; thus, the manners of a
        peasant girl may be graceful, but can hardly be called
        elegant.
        [1913 Webster]

WordNet (r) 3.0 (2006):

elegance
    n 1: a refined quality of gracefulness and good taste; "she
         conveys an aura of elegance and gentility" [ant:
         inelegance]
    2: a quality of neatness and ingenious simplicity in the
       solution of a problem (especially in science or mathematics);
       "the simplicity and elegance of his invention"

Moby Thesaurus II by Grady Ward, 1.0:

184 Moby Thesaurus words for "elegance":
   Babylonian splendor, acquired taste, amenities,
   appreciation of excellence, arabesque, attractiveness, baroque,
   baroqueness, beauteousness, beautifulness, beauty,
   beauty unadorned, bloom, breeding, brilliance, charm, cheeseparing,
   chic, chinoiserie, choiceness, civilities, civility,
   civilized taste, civilizedness, clothes-consciousness, comity,
   convention, courtliness, coxcombry, cultivated taste, cultivation,
   culture, daintiness, dandyism, decencies, decency, decorousness,
   decorum, delicacy, dignity, diplomatic code, discrimination, ease,
   economy, economy of assumption, economy of means, elaborateness,
   elegancies, etiquette, euphemism, euphuism, excellence,
   exquisite manners, exquisiteness, facility, fanciness,
   fastidiousness, fineness, finesse, flamboyance, floridity,
   floridness, flow, floweriness, fluency, foppery, foppishness,
   formalism, formalities, formality, frugality, genteelness,
   gentility, gentlemanlikeness, gentlemanliness, gentleness, glory,
   glow, good breeding, good form, good manners, good taste,
   goody-goodness, goody-goodyism, gorgeousness, grace, gracefulness,
   gracility, graciosity, graciousness, grandeur, grandiosity,
   grandness, handsomeness, imposingness, impressiveness, jauntiness,
   ladylikeness, lavishness, law of parsimony, loveliness, lushness,
   luxuriance, luxuriousness, luxury, magnificence, majesty, manners,
   modesty, mores, moresque, nattiness, natural politeness, neatness,
   niceness, nicety, nobility, ostentation, overelaborateness,
   overelegance, overniceness, overornamentation, overpreciseness,
   overrefinement, parsimoniousness, parsimony, pedantry, pinching,
   plushness, poetry, point of etiquette, polish, politeness,
   politesse, poshness, preciosity, preciousness, precisianism,
   prettiness, proprieties, propriety, protocol, proudness, pudency,
   pudicity, pulchritude, punctilio, purism, quality,
   quiet good manners, refinement, resplendence, richness, ritziness,
   rococo, rules of conduct, scrimping, seemliness, shame, sharpness,
   skimping, sleekness, smartness, smoothness, social code,
   social conduct, social graces, social procedures, social usage,
   sophistication, spiffiness, splendidness, splendiferousness,
   splendor, state, stateliness, stinting, style, subtlety,
   sumptuousness, taste, tastefulness, the beautiful, trimness