Source : Webster's Revised Unabridged Dictionary (1913)

Levirate \Lev"i*rate\ (l[e^]v"[i^]*r[asl]t), Leviratical
\Lev`i*rat"ic*al\ (-r[a^]t"[i^]*kal), a. [L. levir a husband's
   brother, brother-in-law; akin to Gr. dah`r: cf. F. l['e]virat
   leviration.]
   Of, pertaining to, or in accordance with, a law of the
   ancient Israelites and other tribes and races, according to
   which a woman, whose husband died without issue, was married
   to the husband's brother.

         The firstborn son of a leviratical marriage was
         reckoned and registered as the son of the deceased
         brother.                                 --Alford.

Source : WordNet®

levirate
     n : the biblical institution whereby a man must marry the widow
         of his childless brother in order to maintain the
         brother's line