Salt lowers the freezing point of water, as will any solute that impedes the change in phase. When it does so, it affects the phase equilibrium, which has as many molecules melting as refreezing. Any ice and snow that melts cannot refreeze unless a much lower temperature is reached.
Salt is basically an impurity, which, when mixed with snow or ice, causes its freezing point to decrease so that the snow (which ought to freeze at 0°C) freezes at a lower temperature. and effectively causes the snow above that temperature to melt. If you live in an area with a cold and icy winter, you have probably seen salt used on sidewalks and roads to keep them ice-free. The salt works by lowering the melting or freezing point of water. The effect is termed 'freezing point depression'.
When you add salt to water, you introduce dissolved foreign particles into the water. The freezing point of water becomes lower as more particles are added until the point where the salt stops dissolving. For a solution of table salt (sodium chloride, NaCl) in water, this temperature is -21°C (-6°F) under controlled lab conditions. In the real world, on a real sidewalk, sodium chloride can melt ice only down to about -9°C (15°F).
Freezing point depression is a colligative property of water. A colligative property is one which depends on the number of particles in a substance. All liquid solvents with dissolved particles (solutes) demonstrate colligative properties. Other colligative properties include boiling point elevation, vapor pressure lowering, and osmotic pressure.
Sodium chloride isn't the only salt used for de-icing, nor is it necessarily the best choice (although it is usually the cheapest). Sodium chloride dissolves into two types of particles: one sodium ion and one chloride ion per sodium chloride 'molecule'. A compound that yields more ions into a water solution would lower the freezing point of water more than salt. For example, calcium chloride (CaCl2) dissolves into three ions (one of calcium and two of chloride) and lowers the freezing point of water more than sodium chloride.
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