When water begins to freeze, the molecules slow down and clump together, forming a solid mass, which is ice. Moisture from the air or water on the surface of ice is kept in check, because molecules between the two are exchanged at an almost even rate. The molecules escape from the ice into the water or air, and in turn the ice takes in molecules.
When salt or sugar comes in contact with ice, or is added to water that ice is in contact with, it will melt faster. This will prevent ice from drawing in as many water molecules, because there will be salt or sugar molecules in the way. However, water molecules will escape from the ice at the same speed. So, the rate of melting will be higher than usual for a particular temperature. Also, salt and sugar molecules will prevent the formation of the proper geometric arrangements of water molecules needed to form ice.
The science behind this has various applications. However, it is most commonly used in parts of the world that see heavy ice formation during the winter. Roads are salted in order to prevent them from freezing or to melt ice that has formed overnight. This makes roads safer to drive on.