The Collaborative International Dictionary of English v.0.48:

Infallibility \In*fal`li*bil"i*ty\, n. [Cf. F.
   infaillibilit['e].]
   The quality or state of being infallible, or exempt from
   error; inerrability.
   [1913 Webster]

         Infallibility is the highest perfection of the knowing
         faculty.                                 --Tillotson.
   [1913 Webster]

   Papal infallibility (R. C. Ch.), the dogma that the pope
      can not, when acting in his official character of supreme
      pontiff, err in defining a doctrine of Christian faith or
      rule of morals, to be held by the church. This was decreed
      by the Ecumenical Council at the Vatican, July 18, 1870.
      [1913 Webster]

WordNet (r) 3.0 (2006):

papal infallibility
    n 1: belief of the Roman Catholic Church that God protects the
         pope from error when he speaks about faith or morality