Source : Webster's Revised Unabridged Dictionary (1913)

Primogeniture \Pri`mo*gen"i*ture\ (?; 135), n. [LL., fr. L.
   primus first + genitura a begetting, birth, generation, fr.
   genere, gignere, to beget: cf. F. primog['e]niture, L.
   primogenitus firstborn. See {Prime}, a., and {Genus}, {Kin}.]
   1. The state of being the firstborn of the same parents;
      seniority by birth among children of the same family.

   2. (Eng. Law) The exclusive right of inheritance which
      belongs to the eldest son. Thus in England the right of
      inheriting the estate of the father belongs to the eldest
      son, and in the royal family the eldest son of the
      sovereign is entitled to the throne by primogeniture. In
      exceptional cases, among the female children, the crown
      descends by right of primogeniture to the eldest daughter
      only and her issue. --Blackstone.

Source : WordNet®

primogeniture
     n : right of inheritance belongs exclusively to the eldest son