The Caribbean Sea sits between the coast of Central and South America on one side, and the West Indies on the other. The name 'Caribbean' is taken from 'Carib', the name of the indigenous peoples living on the islands when Columbus 'discovered' them in 1492.
In Colonial times, European powers relied on the Caribbean islands for crops, such as sugar and coffee beans, which were in high demand. Maybe that's where the 'bean' bit comes from, though I doubt it. In fact, the value of trade in the Caribbean was one of the big reasons that the Continental Army needed a navy of its own - they needed to be able to disrupt trade there in order to make the Revolutionary War a bigger pain in Britain's pocketbook.