The battery essentially is the power source of the vape pen. It's purpose is to create energy in the form of heat to heat the heating coil.

You press the button to close the circuit with the battery so the battery can create heat.

An atomizer is anything that instantaneously converts a liquid into a vapor. The atomizer used in a vape pen is a heating coil, which heats the e-liquid in a vape pen to such a degree that it quickly vaporizes into an aerosol.

The E-liquid inside the vape pen is essentially the liquid that is heated into the vapor that you inhale. There are many different types of chemicals in vape pens, such as Nicotine, Propylene Glycol, Glycerin, and unknown chemicals in flavorings. There is a cartridge in the vape pen that contains the e-liquid before it is heated.

The mouthpiece is the part of the vape pen that you exhale the aerosol from the vape pen.

The Aerosol is the vapor that the vape pen releases and it travels into your lungs.