I don't know how much scientific language is really necessary to explain this phenomena. It all comes down to a principle called "buoyancy", and can be explained by what is known as "Archimedes' Principle."

What this principle basically states is that a floating object displaces an amount of liquid equal in weight to the weight of the object. This means that the amount of water displaced by a boat, no matter how full that boat is, weighs as much as the boat.

The weight is related to the volume of water displaced by
Weight = (Gravity)*(Density of Water)*(Volume of water displaced)
This is where the dimensions of the boat becomes very important.

The volume of water displaced by the boat is equal to the volume occupied by the part of the boat that is below the surfaces of the water. Once the volume of displaced water is greater than the total volume of the boat, it means that the top of the boat will no longer be above the water and the boat will sink.

In general, things float in water if the density (mass per volume) of the object is less than that of water. Since ships are basically hollow, they are, on average less dense than water and will float.

The next question is: how much of the ship will be above the surface of the water? You can calculate the percentage of the ship that is underwater by comparing the weight of the ship to the weight of the water that is displaced by the volume of the ship that is under the surface.

If you take a ship that has a mass of 1,000,000 kilograms and lower it into the ocean - it is going to sink into the water until it has displaced 1,000,000 kilograms of water or, since water has a density of 1000 kg /m³, until 1000 cubic meters of ship volume is under water.

Hopefully, the total volume of this ship is more than 1000 cubic meters or the ship is going to be in trouble.If you add more weight to the ship, the ship is going to float lower in the water. Obviously it is a bad idea for the top of the ship to be too close to the surface of the water because if the hollow parts of the ship start filling with water, it will become more dense on average and eventually sink.