How deep is the hull of a large ship?

Currently roughly 36 meters is the record. The depth of ships varies largely. Varying length, breadth, and weight, different hull designs, and even the salinity of the water itself, are all contributing factors. It depends on liquid displacement.

It's all about buoyancy. An object submerged in a liquid is acted upon by two distinct forces; the downward force of gravity, and the upward force of buoyancy. If the object weighs more than the water it displaces, it will sink. If it weighs less than the water it displaces, it will float.

If you could hang a ship on one side of a balance. You could add water to a container on the other side. Once they balanced, you would have the amount of water the ship will displace. If you poured that water into a container (shaped exactly like the hull of the ship), it would fill it to exactly the same depth at which that ship would float.