In J.R.R. Tolkien’s The Silmarillion, the island kingdom founded for the Edain is Númenor.
The Edain are the Men who aided the Elves during the wars against Morgoth in the First Age. After Morgoth’s defeat, the Valar rewarded them with an island in the Great Sea. Númenor lies between Middle-earth and Aman, and its first king is Elros, the half-Elven brother of Elrond.
Númenórean civilization becomes powerful through seafaring, craftsmanship, and long life. Over time, many Númenóreans grow resentful of the Elves and fear death. Sauron exploits this pride, eventually becoming adviser to King Ar-Pharazôn and encouraging rebellion against the Valar.
The island is destroyed in the Downfall of Númenor after Ar-Pharazôn’s invasion of Aman. Survivors led by Elendil establish the kingdoms of Gondor and Arnor in Middle-earth. Númenor is therefore the ancestral source of the Dúnedain, rather than another name for Gondor or Arnor.