The fictional island kingdom between Middle-earth and Aman in J.R.R. Tolkien’s mythology is Númenor.
Númenor was created as a reward for the Men who had aided the Elves during the wars against Morgoth in the First Age. The Valar raised the island in the Great Sea, west of Middle-earth and east of Aman. Its people were called the Númenóreans or Dúnedain.
The kingdom grew powerful and wealthy, but its rulers became increasingly preoccupied with avoiding death. Under Ar-Pharazôn, Númenor challenged the authority of the Valar and attempted to sail against Aman. The island was destroyed in a cataclysm, and its survivors founded kingdoms in Middle-earth.
Númenor is therefore connected to the later history of Gondor and Arnor. It is not the same place as Tol Eressëa, an island near Aman associated with the Elves.