NOUN (3)

1. a church associated with a monastery or convent;

2. a convent ruled by an abbess;

3. a monastery ruled by an abbot;

The Collaborative International Dictionary of English v.0.48:

Abbey \Ab"bey\ ([a^]b"b[y^]), n.; pl. Abbeys (-b[i^]z). [OF.
   aba["i]e, abba["i]e, F. abbaye, L. abbatia, fr. abbas abbot.
   See Abbot.]
   1. A monastery or society of persons of either sex, secluded
      from the world and devoted to religion and celibacy; also,
      the monastic building or buildings.
      [1913 Webster]

   Note: The men are called monks, and governed by an abbot; the
         women are called nuns, and governed by an abbess.
         [1913 Webster]

   2. The church of a monastery.
      [1913 Webster]

   Note: In London, the Abbey means Westminster Abbey, and in
         Scotland, the precincts of the Abbey of Holyrood. The
         name is also retained for a private residence on the
         site of an abbey; as, Newstead Abbey, the residence of
         Lord Byron.
         [1913 Webster]

   Syn: Monastery; convent; nunnery; priory; cloister. See
        Cloister.
        [1913 Webster]

WordNet (r) 3.0 (2006):

abbey
    n 1: a church associated with a monastery or convent
    2: a convent ruled by an abbess
    3: a monastery ruled by an abbot

Bouvier's Law Dictionary, Revised 6th Ed (1856):

ABBEY, abbatia, is a society of religious persons, having an abbot or abbess
to preside over them. Formerly some of the most considerable abbots and
priors in England had seats and votes in the house of lords.  The prior of
St. John's of Jerusalem, was styled the first baron of England, in respect
to the lay barons, but he was the last of the spiritual barons.