You all like to use these fancy reverse-flow chillers and immersion heat exchangers and the like to cool your wort; but most of the extract brewers and even some of the all grain brewers tend to just shove the hot pot right into an ice bath in the sink or bath tub. You want to get it cold fast, right? Hence the ice, stirring for circulation, the like.
Wanna have some fun?
Get a test tube. Fill it with straight tap water, put a stopper in the top with a hole and toss in a plastic tube.
Put the test tube into a container of ice water. What do you get? ... cold water, right? Yeah, that's obvious.
Now dump half a cup of salt into the ice bath. Give it a minute or two, and watch what happens...
Water shoots out of the test tube as it fills with expanding, freezing ice! Nice trick, right? How the hell does that happen?
This one's easy: Adding salt to water creates a saline solution. The free salt ions (Na+, Cl-) help loosen frozen water from the surface of the ice--in other words, melts it. But salt water has a lower freezing point than regular water: the ice is being forcefully melted at a lower temperature. What will happen is more of the ice gets melted, dropping the temperature of the entire system--if the freezing point is -4C, then the ice bath becomes -4C instead of 0C.
1g of 0C water takes about 80 calories to turn to ice, and vice versa; with salt water that's above its freezing point, it will lose so many calories just to convert the ice into water... instead of converting 1g ice to water at the expense of 80 calories, it converts i.e. 2g ice to water, losing 160 calories--meaning a temperature drop. Once the temperature reaches the freezing point, it takes as much energy to melt the ice as it does to freeze the salt water--if the salt water cooled more (by melting the ice), it would itself freeze. This prevents the phase change. Thus the ice keeps melting until the temperature reaches the freezing point of the saline solution, and then slowly melts to maintain it.
liquid nitrogen on the other hand freezes things it touches. That's because its boiling point is -192F. When it boils, it absorbs energy off whatever it touches to phase change to gas from liquid, which is the same direction as solid to liquid. It'll cool ice to well below freezing because its boiling point is well lower than ice's freezing point. By contrast, salt water is liquid at the temperature of frozen pure water (i.e. ice is 0C, salt water is liquid at 0C) rather than a gas (it boils above 100C). Because it's able to melt the ice actively (i.e. by charge interaction with the salt ions, rather than just by temperature), the potential difference causes heat flow into the ice. In other words, this all makes sense; it's not voodoo magic.
So while you're at rite-aid buying bags and bags of ice for your ice bath, pick up a sack of Epsom salt too. Dump that in the ice bath and try not to freeze your wort into a solid block.