When a salt is placed in an aqueous medium (i.e. water) a "tug-of-war" immediately begins to take place between the polar water molecules and the ions in the salt. The forces in the tug-of-war are electrostatic and between the ion-ion attractions and the water-ion attractions. If the water-ion attraction win the war then the salt is soluble. If the ion-ion attractions win then the salt is insoluble. Consider table salt (NaCl), it is highly soluble and its solubility can be written as
At the atomic level the ions in the salt are being "solvated" by the water molecules as the animation below suggests (place mouse over the image). Note the orientation of the water molecules to the positive and negative ions. The cage of water molecules around the solvated ion is known as a "hydration" cage.