On an aircraft carrier, the island contains the ship's superstructure, much smaller than that of other warships so it does not interfere with flight operations. It is usually offset to one side of the ship, on the edge, or even extending beyond, the flight deck.
A few early and unsuccessful aircraft carriers were built with no island and really no superstructure. This was impractical, as it provided neither visibility for navigating the ship or overseeing the flight deck.
Some specialized carriers, really conversions or "hermaphrodites" that retained battleship or cruiser functions, still had a conventional superstructure with no island. Roughly half of the deck, however, was cleared of guns to form a small flight deck. This has generally been unsuccessful, although might work in some specialized applications with helicopters and STOVL aircraft.
In recent U.S. carrier designs, there has been an effort to reduce the size of the island, reduce right angles on its surface, and generally improve the stealth characteristics of a ship. While it is impossible for an aircraft carrier to "disappear", the stealthier the ship as a whole, the harder it is for search and weapons control radars to lock onto it. Since the island is the highest part, it is also the highest radar target for airborne radars.