The Collaborative International Dictionary of English v.0.48:

Burgage \Burg"age\, n. [From Burg: cf. F. bourgage, LL.
   burgagium.] (Eng. Law)
   A tenure by which houses or lands are held of the king or
   other lord of a borough or city; at a certain yearly rent, or
   by services relating to trade or handicraft. --Burrill.
   [1913 Webster]

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

BURGAGE, English law. A species of tenure in socage; it is where the king or
other person is lord of an ancient borough, in which the tenements are held
by a rent certain. 2 B1. Com. 82.