In J.R.R. Tolkien’s legendarium, the island kingdom founded by Men between Middle-earth and Aman is Númenor.
Númenor is also called Westernesse and is given to the Edain after the War of Wrath at the end of the First Age. The island lies in the Great Sea between Middle-earth and the Undying Lands. Its people, the Númenóreans, receive unusually long lives and great knowledge from the Valar.
The kingdom grows into a powerful maritime civilization, but its rulers become increasingly resentful of their mortality. Under Sauron’s influence, King Ar-Pharazôn sails against Valinor in an attempt to seize immortality. Eru Ilúvatar then changes the shape of the world, destroys the island, and removes Aman from ordinary sailing.
The survivors establish the realms of Gondor and Arnor in Middle-earth. Númenor is therefore the ancestral source of Aragorn’s royal line. It is not the same as Beleriand, which is a region of the First Age, or Gondor and Arnor, which are later successor kingdoms.