The holder of land or house within a borough.
*term definitions retrieved from orb.net
From The Golden Legend: St. Thomas Becket
S. Thomas the martyr was son to Gilbert Beckett, a burgess of the city of London, and was born in the place where as now standeth the church called S. Thomas of Acre. And this Gilbert was a good devout man, and took the cross upon him, and went on pilgrimage into the Holy Land, and had a servant with his knees.