The Collaborative International Dictionary of English v.0.48:

Importance \Im*por"tance\, n. [F. importance. See Important.]
   1. The quality or state of being important; consequence;
      weight; moment; significance.
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            Thy own importance know,
            Nor bound thy narrow views to things below. --Pope.
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   2. Subject; matter. [Obs.]
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            Upon importance of so slight and trivial a nature.
                                                  --Shak.
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   3. Import; meaning; significance. [Obs.]
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            The wisest beholder could not say if the importance
            were joy or sorrow.                   --Shak.
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   4. Importunity; solicitation. [Obs.]
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            At our importance hither is he come.  --Shak.
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WordNet (r) 3.0 (2006):

importance
    n 1: the quality of being important and worthy of note; "the
         importance of a well-balanced diet" [ant: unimportance]
    2: a prominent status; "a person of importance" [syn:
       importance, grandness]

Moby Thesaurus II by Grady Ward, 1.0:

93 Moby Thesaurus words for "importance":
   account, ascendancy, authority, charisma, charm, clout, concern,
   consequence, conspicuousness, control, credit, distinction,
   dominance, domination, effect, elevation, eminence, enchantment,
   esteem, exaltation, excellence, favor, force, good feeling,
   grandeur, gravity, greatness, high mightiness, hold, import,
   incidental power, influence, influentiality, influentialness,
   insinuation, leadership, leverage, loftiness, magnetism, magnitude,
   mark, mastery, matter, moment, momentousness, nobility, notability,
   note, noteworthiness, outstandingness, personality, persuasion,
   pith, position, potency, power, precedence, predominance,
   preponderance, pressure, prestige, priority, prominence, purchase,
   rank, reign, reputation, repute, rule, salience, say, seniority,
   seriousness, significance, signification, standing, stature,
   status, suasion, sublimity, substance, subtle influence,
   suggestion, supereminence, supremacy, sway, upper hand, value,
   weight, weightiness, whip hand, worth, worthiness