[The Squatter of Amon Rûdh]

You can find that answer in The Lord of the Rings without too much trouble.

'Behold Tol Brandir!' said Aragorn, pointing south to the tall peak. 'Upon the left stands Amon Lhaw, and upon the right is Amon Hen, the Hills of Hearing and of Sight. In the days of the great kings there were high seats upon them, and watch was kept there.

The Fellowship of the Ring, p.410

Then later.

He was sitting upon the Seat of Seeing, on Amon Hen, the Hill of the Eye of the Men of Númenor.

The Fellowship of the Ring, p.416

An earlier draft of this passage is more obvious in its meaning:

But also he sat now upon the seat of Sight which the men of Númenor had made.

HoME VII: The Treason of Isengard, p.374

From what Frodo experiences of its powers in The Fellowship of the Ring, I would guess that the seat simply allows one who sits in it to see widely, but probably not in the same way as the Palantíri. I seems as though the seat of Seeing simply makes the world seem smaller rather than allowing one to view distant events in detail or communicate over large distances. There is also a suggestion that the Ring enhances the seat's powers, which could account for the similarity.

The reference to a watch being kept on Amon Lhaw and Amon Hen suggests that on the two hills one sentry would listen and another look for danger to the Númenorean realms in exile, which I would guess is the reason for the properties described in FotR. Don't forget that the Númenoreans, with whom Tolkien associates the two seats, were almost as skilled as the Elves in such work.