The Collaborative International Dictionary of English v.0.48:

Morganatic \Mor`ga*nat"ic\, a. [LL. matrimonium ad morganaticam,
   fr. morganatica a morning gift, a kind of dowry paid on the
   morning before or after the marriage, fr. OHG. morgan
   morning, in morgangeba morning gift, G. morgengabe. See
   Morn.]
   Pertaining to, in the manner of, or designating, a kind of
   marriage, called also left-handed marriage, between a man
   of superior rank and a woman of inferior, in which it is
   stipulated that neither the latter nor her children shall
   enjoy the rank or inherit the possessions of her husband.
   --Brande & C. -- Mor`ga*nat"ic*al*ly, adv.
   [1913 Webster]

WordNet (r) 3.0 (2006):

morganatic
    adj 1: (of marriages) of a marriage between one of royal or
           noble birth and one of lower rank; valid but with the
           understanding that the rank of the inferior remains
           unchanged and offspring do not succeed to titles or
           property of the superior [syn: morganatic, left-
           handed]