Sunken Treasure Chests are underwater chests that can be found near a Sunken Ship. Not all Sunken Ships will have a chest by them as chests have a 12HR respawn time. The chests often contain items that are meant to be sold to a vendor for 5s-10g+. You must have a Recovery Pouch in order to obtain loot from these chests. Using a Recovery Pouch on the chest will cause it to slowly rise to the surface where it can then be looted by anyone.
As of Patch 1.2, it is widely considered to be a 'waste of time' to hunt for underwater chests as its profit / hr is quite low in comparison to many alternative methods.
Ships such as the Galleon can obtain sonars which allow it to detect any Sunken Ship in its immediate area, making it easier to find sunken chests.
The Profit is still good for no labor usage and it is a lot of fun