The Collaborative International Dictionary of English v.0.48:

Adjuration \Ad`ju*ra"tion\, n. [L. adjuratio, fr. adjurare: cf.
   F. adjuration. See Adjure.]
   1. The act of adjuring; a solemn charging on oath, or under
      the penalty of a curse; an earnest appeal.
      [1913 Webster]

            What an accusation could not effect, an adjuration
            shall.                                --Bp. Hall.
      [1913 Webster]

   2. The form of oath or appeal.
      [1913 Webster]

            Persons who . . . made use of prayer and
            adjurations.                          --Addison.
      [1913 Webster]

WordNet (r) 3.0 (2006):

adjuration
    n 1: a solemn and earnest appeal to someone to do something

Easton's 1897 Bible Dictionary:

Adjuration
   a solemn appeal whereby one person imposes on another the
   obligation of speaking or acting as if under an oath (1 Sam.
   14:24; Josh. 6:26; 1 Kings 22:16).

     We have in the New Testament a striking example of this (Matt.
   26:63; Mark 5:7), where the high priest calls upon Christ to
   avow his true character. It would seem that in such a case the
   person so adjured could not refuse to give an answer.

     The word "adjure", i.e., cause to swear is used with reference
   to the casting out of demons (Acts 19:13).