Emyn Arnen was home to a family of Númenórean nobles, and from them came Húrin, chosen by King Minardil of Gondor to be his Steward. Later, Kings of Gondor only chose their stewards from among Húrin's descendants, and eventually the Stewardship of Gondor became hereditary (the stewards named themselves members of the House of Húrin).
After the events of the War of the Ring, King Elessar granted to Faramir, son of the Steward Denethor II, the Princedom of Ithilien and the Lordship of Emyn Arnen (Faramir also maintained the Office of the Steward, even after he tried to surrender it to King Elessar). Emyn Arnen, being the ancestral home of the Stewards of Gondor, became the official home of the Steward Faramir and his descendants.
Emyn Arnen was a Sindarin for "Hills beside the water".