The island kingdom ruled by Aragorn’s ancestors in J.R.R. Tolkien’s legendarium is Númenor.
Númenor was given to the Edain after the War of Wrath at the end of the First Age. Its people, the Númenóreans, received a long life and great gifts, although they were forbidden to sail to the Undying Lands in the west. Their kings eventually became increasingly proud and resentful of that restriction.
Elendil, a descendant of Númenórean royalty, escaped the island’s destruction with his sons Isildur and Anárion. They founded the realms of Arnor and Gondor in Middle-earth. Aragorn is descended from Elendil through the line of Isildur.
Númenor is therefore not the same as Gondor or Arnor, which were successor kingdoms on the mainland. Valinor is also different: it is a region of Aman, not the island realm destroyed in Númenor’s downfall.