Ships float because of volume. For example if you take on object like a rock and put it in the water, it will sink. But if you increase it's volume(the amount of space indside) it will float. Same with a boat. You take the boat and increase it's volume which makes it less dense than water(lighter) and so it floats.

It is surely a magic but great invention of man. Made made boats and big boats and ships. Ship is a big boat.

Eureka! Archimedes Principle [or it could be Mr Willi's]

Some objects, when placed in water, float, while others sink, and still others neither float nor sink. This is a function of buoyancy. We call objects that float, positively buoyant. Objects that sink are called negatively buoyant. We refer to object that neither float nor sink as neutrally buoyant.

The idea of buoyancy was summed up by Archimedes, a Greek mathematician, in what is known as Archimedes Principle: Any object, wholly or partly immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. The old Greek bloke discovered it while sitting in his bath and is reputed to have ran through the streets excitedly yelling "Eureka!" which I think means I have found it, or something similar.

From this principle, we can see that whether an object floats or sinks, is based on not only its weight, but also the amount of water it displaces. That is why a very heavy ocean liner can float. It displaces a large amount of water.

Thus a diver can adjust his weight v buoyancy to become neutrally buoyant, or it explains why a dry log will float or a waterlogged one might sink.

The short answer is that for any given amount of volume, say a cubic foot to start, that if it's total weight is less than that of a cubic foot of water, salt or fresh depending on where it floats, it stays on the surface. That is why a cement boat will float. For boats in the water, if you measure the weight of a boat then the amount of air contained in that boat, in cubic feet FROM THE WATER LINE TO THE BOTTOM will give you the exact weight of the boat when you multiply it times the weight of the water per cubic foot. Add people to the boat and the hull goes deeper and displaces more cubic feet. It's all density differences. The same principal makes oil float on water and hot air or helium balloons rise.

Some of the answers are very good indeed but let me put it in simple terms. A piece of solid steel will sink but if you make a sheet out of it and shape it to keep water out while it partially sinks into the water it will float!

As mentioned above Archimedes found this principle while taking a bath! Must have been playing with his rubber duckies etc I dunno. But he is said to have yelled Eureka and ran about with much excitement!

As mentioned in previous posts the amount of water the shaped sheet metal will displace will be equal to the weight of that solid steel you started with! That is what gives it buoyancy the water pushes against the steel but the steel will displace just enough water to equal its mass by sinking partially. The trick is to shape the metal so that it displace just enough water to keep floating while providing stability while in motion.

Ships are allowed to sink into water to increase stability or improve their non-tipping. If the ship was mostly on top of water it would tip easily (too large a displacement) due to high center of gravity. Therefore if you let the ship sink into the water then it gives you a lower center of gravity and it wont tip as easily when a wave hits it.

The water is denser so below water line the ship has to be very slippery shaped like aerodynamic but actually designed for water to slip past it!

The above water area is also important for extreme optimal speeds as well as that area will be reacting to wind currents!

BTW ships can even be made out of almost any water proof material or the material may be treated to be water proof. There is an annual contest that many universities enter in which they make a canoe out of cement and actually have to paddle it in a race to win prizes!

Naval architecture is a neat and interesting field.