Why do we use salt to melt ice?
(Q&A by Brian Dicks)

Why do we add salt to snow and ice to make them melt? Also, after the snow and ice have melted, why don’t they just refreeze?
Water molecules can evaporate even in the form of ice. When the molecules evaporate, they form a vapor above the surface of the water or ice and the vapor molecules exert pressure on the solid or liquid surface. This is called vapor pressure.
Salt is a nonvolatile substance; it does not vaporize or evaporate. If you add a salt to water, the vapor pressure of the water is lowered. This is because the presence of a nonvolatile substance in water reduces that water's surface area. The salt particles, which do not evaporate, are taking up spots on the surface of the water, leaving fewer water molecules free to escape through evaporation.
If you've ever watched water boil, you would have seen the steam escaping off the surface at the boiling point. At the boiling point, the vapor pressure of the water reached the pressure of the air. If, however, you reduced the surface area of the water in the pot by adding salt, it then takes a higher temperature for water to reach its boiling point. The boiling point of 1000 grams of water with 58.5 grams of table salt in it is 100.515 degrees Celsius, not 100.000 degrees Celsius.
The same principle holds true for freezing. In order for water to freeze, the vapor pressure of ice and liquid water must be equal. By adding salt to water. we lower water's vapor pressure. Since water freezes when both vapor pressures are equal, water must now must reach a lower temperature for this to occur. The freezing point of 1000 grams of water with 58.5 grams of salt in it is -1.853 degrees Celsius, not 0.000 degrees Celsius.

Source: Merrill Chemistry by Smoot, Smith, and Price; Glencoe Publishing, 1998.