What is the purpose of sprinkling common salt on ice?

The melting point of ice decreases by adding salt to ice.

Actually, salt lowers the freezing/melting point of water, so in both cases the idea is to take advantage of the lower melting point.

Ice forms when the temperature of water reaches 32 degrees Fahrenheit (0 degrees Celsius). When you add salt, that temperature drops: A 10 percent salt solution freezes at 20 F (-6 C), and a 20 percent solution freezes at 2 F (-16 C). On a roadway, this means that if you sprinkle salt on the ice, you can melt it. The salt dissolves into the liquid water in the ice and lowers its freezing point.