Based on Archimedes' Principle, water exerts an upward buoyant force on an object as it is placed in water. This force is equal to the weight of the water being displaced by the object. The object's mass is constant, but weight is relevant to gravity, therefore the object feels lighter.
Another way of explaining Archimedes' Principle is that an object in water has two forces acting on it at once. Gravity is pulling the object down, while buoyancy is pushing the object up, which makes the object feel lighter. If the object sinks, it still weighs less the amount of the water it has displaced.