Depending on the suffix used, Okinawa (沖縄) can refer to the prefecture (-ken, 県), its enclosing archipelago (-rettō, 列島), the main island (-hontō, 本島) or the eponymous city on the main island (-shi, 市); but when most visitors say they're 'going to Okinawa', they mean they're visiting the Southwest Islands.
Formerly the seat of power of the Ryūkyū dynasty, Okinawa-hontō is the largest island in the Nansei-shotō (Southwest Islands) and its capital, Naha, the busiest city. If Tōkyō were a pie, and you cut a tiny slice, dropped it on an island in the Pacific, and served it with a dollop of Florida, Naha might be what you'd get. Most visible traces of Ryukyū culture were obliterated in WWII, and there remains a huge US military presence on the island.
In spite of this, the Ryūkyū lineage remains strong and is evident in Okinawa's unique culinary, artistic and musical traditions.