A piece of land given to a vassal by a lord is called a fief. The giving of fiefs in return for promised military support was a defining aspect of feudalism, a system of social organization common in Europe between the ninth and 15th centuries A.D.
Technically, the lord did not actually give the land itself to his vassals, but rather gave them the right to use the land and retain income produced by the land. The vassals were responsible for providing aid to their lord in battle or giving him counsel if summoned. Eventually, the obligation of military service diminished as vassals began paying the lord in lieu of serving. With this money, the lord hired mercenaries to fight in place of his vassals. "Fee" is an alternate term for "fief."