The Collaborative International Dictionary of English v.0.48:

Reconvention \Re`con*ven"tion\ (-v?n"sh?n), n. (Civil Law)
   A cross demand; an action brought by the defendant against
   the plaintiff before the same judge. --Burrill. Bouvier.
   [1913 Webster]

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

RECONVENTION, civ. law. An action brought by a party who is defendant
against the plaintiff before the same judge. Reconventio est petitio qua
reus vicissim, quid ab actore petit, ex eadem, vel diversa causa. Voet, in
tit. de Judiciis, n. 78; 4 N. S. 439. To entitle the defendant to institute
a demand in reconvention, it is requisite that such demand, though different
from the main action, be nevertheless necessarily connected with it and
incidental to the same. Code of Pr. Lo. art. 375; 11 Lo. R. 309; 7 N. S.
282; 8 N. S. 516.
     2. The reconvention of the civil law was a species of cross-bill.
Story, Eq. Pl. Sec. 402. See Conventio; Bill in chancery. Vide Demand in
reconvention.