Domain

A Domain is the territory controlled by a particular House.

Codex
"The domain of a house is the region it controls, i.e. the domain of; - a ruling house is the colony - a leading house is the faction - a great house is the league

For easier navigation, when you click on a leading or great house's flag, you are shown information about that house's domain (i.e. its faction or league) as well as information about the house."