Anórien was a region and fiefdom of Gondor.
Geography
When Isildur and Anárion divided the South Kingdom of Gondor among them Anárion took the region between the river Erui and the river Anduin to Mount Mindolluin and then west to the Firienholt (back then called the North Wood). Thus Anórien originally included Minas Tirith (back then called Minas Anor) and the land between the river Erui and the river Anduin. It is unknown if and when the land between the eastern end of the White Mountains and the river Anduin between the falls of Rauros and the river Erui ceased to be a part of Anórien and if the land between the Erui and the Anduin became a part of Lebennin, Lossarnach or another region.
After Calenardhon was given to the Éothéod to become the Kingdom of Rohan, the western borders of Anórien were the Mering Stream and the Mouths of the Entwash, the Anduin and the west-cliffs of the Emyn Muil.
The land contained the Drúadan Forest and fertile farmlands. The Great West Road traversed the fief. The Warning beacons of Gondor were located to the south of the road.
During the Elder Days, the region was occupied by Pre-Númenóreans. These were separated relatives of the House of Haleth while the Edain migrated to the west during the late First Age. The aboriginal Woses fled to the forests of that region, hunted by the Men of Darkness.
At the end of the Second Age, the region was given to Anárion as part of the Realms in Exile and was named 'Anórien' after him. Anárion built Minas Anor on Amon Tirith of the Mindolluin.
Peoples from Anórien, as well as from Ithilien and Calenardhon joined with Eldacar against Castamir in the Kin-strife.
As the Great Plague spread, cities were evacuated and many fled to Ithilien and Anórien.
Steward Túrin II fortified the isle of Cair Andros to defend Anórien.
By the time of the War of the Ring, Anórien was one of the few fiefs which was dominated by the Dúnedain of Gondor; specifically, in Minas Tirith and the adjacent townlands where Sindarin was still known and used as a daily language. It would appear that the western part of Anórien (from Min-Rimmon westward) was deserted or depopulated by this time, as tidings of the coronation of Aragorn went out into "all parts of Gondor, from Min-Rimmon even to Pinnath Gelin and the far coasts of the sea".
When Sauron released a secondary force from the Morannon, they overwhelmed the defenders of Cair Andros, and used the island to cross into Anórien. They blocked the eastward progress of the Rohirrim as they rode to Gondor's aid, though after the Battle of the Pelennor Fields, Elfhelm and 3000 Rohirrim chased them down and pushed them back out of Anórien.