The Battleship is a powerful sea unit, added in the "Power" update. It is unlocked with Navigation, and is the upgrade of Ship, having overall better stats. For a 15-star fee, you can upgrade an individual ship into a battleship. Battleships can move onto land from water tiles, but when you move back onto water via ports, the unit will become a boat again. You can also receive battleships as rewards via Ruins.
Exploring. The Battleship's high movement speed and large line of sight means that exploration on the sea is easier than ever! As soon as you find land or a village, you can send a less expensive boat or ship to go explore it while your battleship focuses on other things.
Heavy Bombardment from Sea. If one of these rolls up in your waters, it's probably not coming to sit down and talk over a tea with you. It means business. With the damage of a catapult and the defence of a defender, this beast is the ultimate destroyer. It can wipe out entire forces from the coast, clearing a path for your armies to invade.
Quick and Powerful Retaliation. Someone's ship just attacked your giant in a boat? Got 20 stars to spare? Ship upgrading is like upgrading to Veteran: it does not consume your attack. If you're in a quick fix, you can max your boat instantly and make whoever dared touch you pay dearly!
Battleships aren't good for:
Transport/Capturing Cities. The Battleship's high cost means that it would be a huge waste of resources to spend 20 stars on a warship, then blow it all when you land. Even if there is an open city, it is usually not a good idea to land with a battleship. Better to use cheaper ships or boats instead.
Score. Each of the other tier 3 units grants you score proportional to their resource cost. But resources sunk into ship or battleship upgrades are "wasted" in score terms. Near the end of a Perfection game, be careful not to do more Battleship upgrades than you need, as you get no direct return on the investment.