The Collaborative International Dictionary of English v.0.48:

Earldom \Earl"dom\, n. [AS. eorl-d?m; eorl man, noble + -d?m
   -dom.]
   1. The jurisdiction of an earl; the territorial possessions
      of an earl.
      [1913 Webster]

   2. The status, title, or dignity of an earl.
      [1913 Webster]

            He [Pulteney] shrunk into insignificancy and an
            earldom.                              --Chesterfield.
      [1913 Webster]

WordNet (r) 3.0 (2006):

earldom
    n 1: the dignity or rank or position of an earl or countess
    2: the domain controlled by an earl or count or countess

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

EARLDOM. The seigniory of an earl; the title and dignity of an earl.