The firma was a payment made by a farmer, or lessee, as the annual render from a manor.
The farms of royal manors were often held by sheriffs. Other land held at farm after the Conquest was leased in return for a fixed rent. The majority of such leases recorded in Domesday Book were for sums in excess - often greatly in excess - of the stated value of the estate in 1086. Such leases were often held by Englishmen and probably represent Norman lords using the expertise of the natives to maximise the profits from their new estates. The burden, of course, would ultimately have fallen upon the manorial peasantry.
For more information on such leases, see Reginald Lennard, Rural England, 1086-1135: a study of social and agrarian conditions (1959).
See also codes for miscellaneous items.