Sodium chloride -- better known as rock salt -- helps to melt ice, or at least loosen it enough to make chipping it away easier. Rock salt accomplishes this by lowering the freezing point of water. Rock salt is effective at melting ice at temperatures down to 5 degrees Fahrenheit, although its effectiveness begins to wane at around 15 degrees.
As rock salt melts ice, it also corrodes a variety of surfaces, including the bodies and metal underbellies of automobiles, metal siding on houses and the very concrete and asphalt that driveways are made from. Heavy use of rock salt can take years off your driveway, causing it to need refinishing more often and replacement sooner than other driveways.
Rock salt's popularity is due in part to simple economics -- it remains one of the cheapest deicers on the market. But a number of alternatives are available, many of which are less damaging. You can sprinkle sand or kitty litter on your driveway. While they do not affect the freezing point of water, they absorb heat, which helps to loosen ice. Warm water can work, too, if the air temperature isn't too cold. A number of alternative deicers are also available, and some, such as calcium chloride and magnesium chloride, are less damaging to asphalt and concrete.
Even if you do not use rock salt, the simple action of water freezing can damage driveways, sidewalks and roads. Water makes its way into preexisting holes, cracks and imperfections; when it freezes, it expands and causes the cracks to widen and the holes to get bigger. In a sense it's just a price you pay for living in a cold climate, but steering away from corrosive rock salt can significantly lessen the damage to your driveway and extend its life expectancy.