Amon Hen (Sindarin for 'Hill of the Eye') was constructed in the early days of Gondor, perhaps even as early as the Second Age, its other names in Westron were The Hill of Sight and the Hill of the Eye. Aragorn says that it and its counterpart hill were made '...in the days of the great kings' (The Fellowship of the Ring II 9) but this is open to interpretation.
The hill towers above the western banks of the Anduin, and it is one of the 3 peaks at the southern end of the long lake Nen Hithoel above the Falls of Rauros on the Anduin River. The other two hills being Amon Lhaw and Tol Brandir. The Seat of Seeing (Amon Lhaw, the Hill of the ear and the "seat of hearing") was built there, close to the earlier northern borders of Gondor, serving as a watchtower for the borders of Gondor.
The Company of the Ring passed by Amon Hen after having travelled down the Anduin, and it was here that the fellowship broke up as a result of Boromir's death, with Frodo and Sam crossing the river on their way east to Mordor. Frodo sits on the Seat of Seeing and immediately he is able to see telescopically for hundreds of miles in all directions because of its magical properties.