Salt melts ice by lowering the melting point of water. Pure water changes into ice at 32 degrees Fahrenheit. When salt is added to water, the melting point drops. If the temperature is above the new melting point, then the ice starts to melt; however, if the temperature is below the new melting point, the addition of the salt has no effect.
Ice usually has a thin layer of water coating its surface. Molecules from the ice are constantly slipping off the ice and escaping into the liquid water (melting). At the same time, molecules from the water are continually getting stuck on the solid ice (freezing). When the temperature of the ice is 32 degrees Fahrenheit, the processes happen at the same rate and the amount of ice and water doesn’t change.
When salt is added to the water-coated ice, it dissolves into the liquid water but not into the solid ice. This affects the balance between the freezing and melting rates. Now there are fewer water molecules available to stick to the solid ice, but the number of ice molecules available to escape into the liquid water remains the same. This means that the rate of melting begins to exceed the rate of freezing, so overall the ice starts to melt.