Calcium chloride makes ice melt because it lowers the freezing point of water. When water is mixed with any salt, its freezing point descends below 32 degrees Fahrenheit, so it remains liquid at colder temperatures.
Any salt helps ice melt. Calcium chloride is a particularly good choice because it is made up of three molecules, one of calcium and two of chlorine. Many salts have only two molecules, and the more molecules a salt has, the more the freezing point will be depressed. In addition, calcium chloride has a remarkably high enthalpy of solution, which means when it is mixed with water, it gives off heat, which in turn helps to melt more ice to mix with the salt.