Piracy is said to have exploded in the Caribbean during this time because of the ending of the War of Spanish Succession. When this war ended, large numbers of trained sailors were put out of work as countries reduced the sizes of their navies. At the same time, there was a boom in cross-Atlantic trade with the ending of the war. These conditions made for a golden age in piracy.
Rich cargoes were being shipped during this period, particularly with the boom in the triangular slave trade. Much of this went through the Caribbean. With navies shrinking in size, it was much harder for European countries to patrol the area effectively. This meant that there were many experienced naval fighters, with rich treasures to be taken, in an area that was hard to patrol.
These factors, not surprisingly, led to a golden age of piracy in the Caribbean.