Ok, the first concept to wrap our heads around is that the melting and freezing point of any liquid is just about the same. Water freezes at 32 degrees Fahrenheit, but it will also melt any smidgen of a degree above that. Make sense?
The next thing to understand is that ice cream freezes (and melts!) at a lower temperature than water. The sugar and fats in the mix interfere with the formation of ice crystals, and it takes a colder temperature to get the ice cream to really freeze. Therefore, we can’t use straight ice to chill the ice cream base, because the ice will melt before the base gets cold enough.
Salt provides the solution. Similar to sugar, salt affects how water freezes and effectively lowers the freezing/melting point of water. Creating a saltwater slush and packing this around our ice cream base allows us to cool the base enough so that it starts to thicken and freeze before the ice melts completely.
This whole process feels very counter-intuitive to us! We’re looking at a slushy, half-melting saltwater mix and thinking that it can’t possibly be colder than hard ice cubes. But amazingly, it is. And what’s more, it works to make ice cream and has done so for centuries!