The great island kingdom destroyed before Aragorn’s ancestors reached Middle-earth was Númenor in J.R.R. Tolkien’s mythology.
Númenor was an island kingdom granted to the Men who had aided the Valar in the War of Wrath. Its people became renowned for long life, seafaring, and power. Over time, fear of death and resentment toward the immortal Elves contributed to Númenor’s moral and political decline.
King Ar-Pharazôn eventually challenged the Valar by sailing west toward Aman. In response to this rebellion, Eru Ilúvatar changed the shape of the world and destroyed Númenor in the event remembered as the Downfall of Númenor. Elendil and his sons escaped the catastrophe and founded kingdoms in Middle-earth.
Númenor is not Valinor, the realm of the Valar, and it is not Beleriand, the First Age region later destroyed in the War of Wrath. Its survivors are the ancestors of the Dúnedain, including Aragorn.