Since ice cream mix begins to freeze at 27 Fahrenheit (-3 Celsius), the container in the ice cream maker must be cooled to, or below, that temperature. Ice made from regular water is inadequate for cooling the container. That's because once the ice melts, the meltwater is warmer than 32 Fahrenheit (0 Celsius).
Salt water, however, has a lower freezing temperature than regular water; a saturated salt solution freezes at -6 Fahrenheit (-21 Celsius) (saturated means the water contains the greatest possible amount of salt in solution).
When salt is put on ice, it dissolves on the ice's watery surface. In the process, heat is absorbed. The salt also causes the ice to melt quickly—another process that absorbs heat from the surroundings. The slushy ice/salt mixture remains well below the temperature necessary to freeze ice cream.