For a longer more detailed explanation please refer to a post on the blog titled: How do Electronic Cigarettes Work?
Electronic cigarettes, cigars and pipes (from here on just referred to as electronic cigarettes) consist of 3 components: a battery, an atomizer and a nicotine cartridge. When a person takes a drag the atomizer and the light on the tip is powered on by the battery. The atomizer heats the air drawn into the electronic device to a high enough temperature that it vaporizes the liquid nicotine solution in the replaceable nicotine cartridge. The vapor is then inhaled into the mouth and lungs fully simulating the smoking experience and satisfying the craving smokers seek. The simulated “smoke” is actually just water vapor that evaporates in a few seconds and leaves no lingering odor.