Since non-polar substances are held together by weak van der Waals interactions and water molecules use strong hydrogen bonds, the van der Waal interactions of non-polar substances are not strong enough to break the hydrogen bonds of the water molecules. Accordingly, the non-polar substance cannot disperse itself in water.
Water is a polar molecule because it is made up of hydrogen and oxygen, which have different electronegativities. The electronegativity of an atom is its tendency to pull the bonded pair of electrons closer to itself, thereby giving the atom a partial negative charge. Oxygen has a higher electronegativity than hydrogen and pulls the bonded electrons towards itself, which gives oxygen a partial negative charge and the hydrogen atoms a partial positive charge. The oxygen that one water molecule has exerts an attractive force, which is called a hydrogen bond, on a hydrogen atom of a different water molecule.
Hydrogen bonds can only be disrupted by other polar molecules, which have a partial positive charge and a partial negative charge. The partial charges give the polar molecule the ability to insert itself between water molecules and thus disperse across the solution. This dispersion is what is known as solubility.
Non-polar substances are held together by weak-induced dipole moments. These are called van der Waals forces. They are constantly fluctuating and are temporary dipoles, unlike water and other polar substances, which are stronger, permanent dipoles. The force exerted by the van der Waals interactions is not strong enough to disrupt the hydrogen bonds between the water molecules. This means the non-polar molecules cannot insert themselves between water molecules and remain isolated, or insoluble, in water.