When cooling water there is a relatively linear relationship between energy removed and drop in temperature. Until you hit freezing point, then, while you remove energy the temperature does not actually drop. The loss in energy comes from changing the structure of the water to one with a lower energy state, that being ice. The more energy you remove the higher the ratio of liquid water to solid water. That's slush.
Adding the salt essentially causes the water to turn from solid to liquid, but it has the same total amount of heat energy in it which requires that the temperature drops. Or another way to look at it, turning the ice into water costs "heat" which means the solution becomes cooler.
Roughly, I'm sure a chemist would argue about the exact semantics and processes, but good enough for Jr. high level chemistry.