A cannonball barrel-boat is an item made during the quest, A Clockwork Syringe. Once made, it's used with the cannon on Bill Teach's ship, The Adventurous, to shoot players over the sea from the ship to Bloodsplatter Isle.
With the tinderbox in your inventory, use the gunpowder on the chain to make a heated chain. Next, use the heated chain on the anvil (found at the tail-end of the ship) to make a fused cannonball and chain. Use the cannonball and chain on the barrel lastly to make the cannonball barrel-boat. The extra gunpowder is required to light the cannon on the top deck to propel the cannonball barrel-boat to open sea.