A Simple Explanation

Despite the name "canned air," the cans actually contain gases that are much easier to compress into liquids, such as tetrafluoroethane, difluoroethane, or trifluoroethane. The can actually contains liquids that boil as they are released from the can creating an endothermic reaction which as we all know absorbs heat. So the trainers are using them to rapidly cool an injured area. The main components of air, which are oxygen and nitrogen, are in fact very rarely used for this application. Have you ever cooked on a gas grill and felt of the propane tank? The tank gets cold as the liquid propane converts/boils and is released as a gas to be burned in the grill. Propane or Butane can also be used to cool but they are extremely flammable.