Insoluble substances do not dissolve in water.
The general rule is that "like dissolves like." Meaning that polar compounds tend to dissolve polar and ionic compounds because they are close in terms of intermolecular forces.
But water does not dissolve nonpolar molecules, because water in this case would be much more attracted to itself than to the nonpolar molecules.
There are also the solubility rules, which tell you what will and won't dissolve in water.