Salt is commonly known by the chemical formula NaCl, or sodium chloride. When NaCl is mixed with water (H2O), the Na cations (positive ions) and Cl anions (negative ions) mix with the H cations and OH anions of the H2O to form a new solution. This solution causes the freezing point of the water to lower--that is, any solution that is above that freezing point will not freeze. Therefore, it is harder for ice to form unless it is cold enough to be below the new freezing point. The salt lowers the freezing point by altering the rate at which water molecules attach to the ice, causing the point at which ice and water molecules are switching places at the same rate (the freezing point) to decrease.
There are limitations, however: once enough salt has been added to lower the freezing point to 0 degrees Celsius, the water will have reached its limit as to how much salt it can dissolve, and the freezing point can not be further lowered.