It may surprise you, but the heat exchanger in commercial aircrafts are VERY simple to understand because it follows the laws of physics (or is it chemistry? lol)
When two fluids (or gases in this case) of different temperatures come in contact, heat is transfered from the hotter fluid to the cooler one.

So it basicly means that hot, high pressure bleed-air is routed through the heat exchanger and is cooled by outside air coming from the ram-air intake.

This step is one of many in the process of an Air Cycle Machine. Feel free to search the web for more info on ACM's