The great island kingdom destroyed beneath the sea in Tolkien's legendarium is Númenor.
Númenor was granted to the Edain after the First Age as a reward for their aid against Morgoth. Its people, the Númenóreans, enjoyed long lives and became renowned as sailors, builders, and rulers. Their island lay between Middle-earth and the Undying Lands.
Over time, fear of death, imperial ambition, and resentment toward the immortal Elves grew among many Númenóreans. Sauron exploited these tensions after allowing himself to be taken to the island as a prisoner. Under the rule of Ar-Pharazôn, the king's invasion of the Undying Lands brought catastrophic judgment.
The destruction occurred in the Second Age, when Eru Ilúvatar changed the shape of the world and submerged Númenor. Elendil and his sons escaped with the Faithful and founded the kingdoms of Arnor and Gondor in Middle-earth.