The Collaborative International Dictionary of English v.0.48:

Exequatur \Ex`e*qua"tur\, n. [L., 3d pers. sing. pres. subj. of
   exequi, exsequi, to perform, execute.]
   1. A written official recognition of a consul or commercial
      agent, issued by the government to which he is accredited,
      and authorizing him to exercise his powers in the place to
      which he is assigned.
      [1913 Webster]

   2. Official recognition or permission. --Prescott.
      [1913 Webster]

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

EXEQUATUR, internat. law. A declaration made by the executive of a
government near to which a consul has been nominated and appointed, after
such nomination and appointment has been notified, addressed to the people,
in which is recited the appointment of the foreign state, and that the
executive having approved of the consul as such, commands all the citizens
to receive, countenance, and, as there may be occasion, favorably assist the
consul in the exercise of his place, giving and allowing him all the
privileges, immunities, and advantages, thereto belonging. 3 Chit. Com. Law,
56; 3 Maule & Selw. 290; 5 Pardes. 1445.



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

EXEQUATUR, French law. This Latin word was, in the ancient practice, placed
at the bottom of a judgment emanating from another tribunal, and was a
permission and authority to the officer to execute it within the
jurisdiction of the judge who put it below the judgment.
     2. We have something of the same kind in our practice. When a warrant
for the arrest of a criminal is issued by a justice of the peace of one
county, and he flies into another, a justice of the latter county may
endorse the warrant and then the ministerial officer may execute it in such
county. This is called backing a warrant.