An island/continent that originally existed west of Middle-Earth. The Valar founded Valinor in the center of the island after the destruction of their original home, Almaren. Here they dwelt with the Calaquendi elves.
To protect the island the Valar raised the Pelóri (Mountains of Defence) and made the seas between Aman and Middle-Earth difficult to traverse.
After Ar-Pharazôn of Númenor attempted to overtake the island in II 3319 (after being persuaded to do so by Sauron), the Valar removed the island from Arda (also destroying Númenor while they were at it) and it can now only be reached by Elves (or, on occasion, equally special individuals, such as the Ring Bearers and members of the Fellowship of the Ring for example).
Aman (or the Blessed Realm) is where all Elves (or any aforementioned special cases) go to live out the remainder of their lives in eternity. It is reached by sailing from the Grey Havens with Círdan the Shipwright.
The Undying Lands of Aman is "kind of like" the J.R.R. Tolkien equivalent of Heaven.
(see J.R.R. Tolkien and read The Lord of the Rings)