Dominium, lordship in the Phillimore translation, is often translated as demesne.
Lordship had two related meanings. In a general sense, it indicated title to a holding. Phrases such as 'is and always was in the lordship of the abbey of Ely' were statements of title, of ownership.
The word lordship was also used in a restricted sense to refer to the part of his holding farmed by the lord himself, or by his servants on his behalf, as opposed to the land of the peasants. At a later date, the lord's demesne, or lordship land, would be known as his home farm.
For more detail on the lord's demesne, see Rosamond Faith, The English peasantry and the growth of lordship (1997).