The Collaborative International Dictionary of English v.0.48:

Possibility \Pos`si*bil"i*ty\, n.; pl. Possibilities. [F.
   possibilit['e], L. possibilitas.]
   1. The quality or state of being possible; the power of
      happening, being, or existing. "All possibility of error."
      --Hooker. "Latent possibilities of excellence." --Johnson.
      [1913 Webster]

   2. That which is possible; a contingency; a thing or event
      that may not happen; a contingent interest, as in real or
      personal estate. --South. Burrill.
      [1913 Webster]

WordNet (r) 3.0 (2006):

possibility
    n 1: a future prospect or potential; "this room has great
         possibilities"
    2: capability of existing or happening or being true; "there is
       a possibility that his sense of smell has been impaired"
       [syn: possibility, possibleness] [ant: impossibility,
       impossibleness]
    3: a tentative insight into the natural world; a concept that is
       not yet verified but that if true would explain certain facts
       or phenomena; "a scientific hypothesis that survives
       experimental testing becomes a scientific theory"; "he
       proposed a fresh theory of alkalis that later was accepted in
       chemical practices" [syn: hypothesis, possibility,
       theory]
    4: a possible alternative; "bankruptcy is always a possibility"
       [syn: possibility, possible action, opening]