The Collaborative International Dictionary of English v.0.48:

Hilary term \Hil"a*ry term`\
   Formerly, one of the four terms of the courts of common law
   in England, beginning on the eleventh of January and ending
   on the thirty-first of the same month, in each year; -- so
   called from the festival of St. Hilary, January 13th.
   [1913 Webster]

   Note: The Hilary term is superseded by the Hilary sittings,
         which commence on the eleventh of January and end on
         the Wednesday before Easter. --Mozley & W.
         [1913 Webster]

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

HILARY TERM, Eng. law. One of the four terms of the courts, beginning the
11th and ending the 31st day of January in each year.