Whenever you commit acts of piracy such as plundering and boarding ships, your wanted level is increased and a bounty is placed on the Jackdaw
As your wanted level gets higher, tough Hunter Ships are dispatched to hunt you down; these Hunter Ships possess superior weapons and a stronger hull than an average ship, and are equipped specifically to fight pirates
To reset your Wanted Level, talk to a corrupt Local Officer who would be happy to take care of things if you give him a high enough bribe.