The Collaborative International Dictionary of English v.0.48:

Delicacy \Del"i*ca*cy\, n.; pl. Delicacies. [From Delicate,
   a.]
   1. The state or condition of being delicate; agreeableness to
      the senses; delightfulness; as, delicacy of flavor, of
      odor, and the like.
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            What choice to choose for delicacy best. --Milton.
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   2. Nicety or fineness of form, texture, or constitution;
      softness; elegance; smoothness; tenderness; and hence,
      frailty or weakness; as, the delicacy of a fiber or a
      thread; delicacy of a hand or of the human form; delicacy
      of the skin; delicacy of frame.
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   3. Nice propriety of manners or conduct; susceptibility or
      tenderness of feeling; refinement; fastidiousness; and
      hence, in an exaggerated sense, effeminacy; as, great
      delicacy of behavior; delicacy in doing a kindness;
      delicacy of character that unfits for earnest action.
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            You know your mother's delicacy in this point.
                                                  --Cowper.
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   4. Addiction to pleasure; luxury; daintiness; indulgence;
      luxurious or voluptuous treatment.
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            And to those dainty limbs which Nature lent
            For gentle usage and soft delicacy?   --Milton.
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   5. Nice and refined perception and discrimination; critical
      niceness; fastidious accuracy.
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            That Augustan delicacy of taste which is the boast
            of the great public schools of England. --Macaulay.
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   6. The state of being affected by slight causes;
      sensitiveness; as, the delicacy of a chemist's balance.
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   7. That which is alluring, delicate, or refined; a luxury or
      pleasure; something pleasant to the senses, especially to
      the sense of taste; a dainty; as, delicacies of the table.
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            The merchants of the earth are waxed rich through
            the abundance of her delicacies.      --Rev. xviii.
                                                  3.
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   8. Pleasure; gratification; delight. [Obs.]
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            He Rome brent for his delicacie.      --Chaucer.

   Syn: See Dainty.
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WordNet (r) 3.0 (2006):

delicacy
    n 1: the quality of being beautiful and delicate in appearance;
         "the daintiness of her touch"; "the fineness of her
         features" [syn: daintiness, delicacy, fineness]
    2: something considered choice to eat [syn: dainty,
       delicacy, goody, kickshaw, treat]
    3: refined taste; tact [syn: delicacy, discretion]
    4: smallness of stature [syn: delicacy, slightness]
    5: lack of physical strength [syn: fragility, delicacy]
    6: subtly skillful handling of a situation [syn: delicacy,
       diplomacy, discreetness, finesse]
    7: lightness in movement or manner [syn: airiness, delicacy]