This likely denotes the domain of the "king of Uí Briúin", a title borne primarily by men of the Uí Briúin Seóla. As Knox points out, these kings were distinguished at an early date from the Síol Muireadaigh of central Roscommon in the Book of Rights, suggesting that the lands of the Uí Briúin Seóla were the original "Hy Briuin".
This likely pertains to the territory ruled by the "king of Uí Briúin", a title usually reserved for men from the Uí Briúin Seóla. Knox observes that these kings were distinguished in early records from the Síol Muireadaigh, who inhabited central Roscommon, suggesting that the lands of the Uí Briún Seóla were historically referred to as "Hy Briuin".