The Bahamas is a collection of more than a hundred islands, only a couple dozen of which are inhabited. Some of the very small ones are privately owned; Half Moon Cay was owned by Holland America Lines and has been owned by Carnival since Carnival acquired Holland America. The ships are too big to dock there, you have to take a tender in to a small dock.
There's a nice dock, several nice buildings (all with the goal of separating you from your money!), and plenty of deck chairs on the beach. Carnival does a good job of making sure the passengers who visit the "private island" have an enjoyable time. The barbecue lunch--how did they feed so many, so quickly, with so few?!
View of Half Moon Cay from atop Carnival Victory, 2/20/2014 from Darren Miller on Vimeo.