How do elephants lose heat from their ears?

One important reason for elephants flapping their ears is to regulate their body temperature. Elephant ears have an extensive network of blood vessels all over them. When it is hot they flap their ears which cause air to move across them. This in turn cools the surface blood vessels; this cooler blood then circulates around the elephant's body. The temperature of the blood passing through the ears can be reduced by as much as ten degrees Fahrenheit before being returned to the body. Elephants that originated in warmer climates have bigger ears then those that belong in cooler conditions.

They are also used as a display of aggression to make the elephant look bigger in an effort to intimidate predators or rivals. It is also theorised that they are used to fan a scent produced by the musth gland (which is just behind the eyes)