The Collaborative International Dictionary of English v.0.48:

Orphanage \Or"phan*age\, n.
   1. The state of being an orphan; orphanhood; orphans,
      collectively.
      [1913 Webster]

   2. An institution or asylum for the care of orphans.
      [1913 Webster]

WordNet (r) 3.0 (2006):

orphanage
    n 1: the condition of being a child without living parents; "his
         early orphanage shaped his character as an adult" [syn:
         orphanage, orphanhood]
    2: a public institution for the care of orphans [syn:
       orphanage, orphans' asylum]

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

ORPHANAGE, Eng. law. By the custom of London, when a freeman of that city
dies, his estate is divided into three parts, as follows: one third part to
the widow; another, to the children advanced by him in his lifetime, which
is called the orphanage; and the other third part may be by him disposed of
by will. Now, however, a freeman may dispose of his estate as he pleases;
but in cases of intestacy, the statute of distribution expressly excepts and
reserves the custom of London. Lov. on Wills, 102, 104; Bac. Ab. Custom of
London, C. Vide Legitime.