A microwave is a small oven that cooks or heats food very quickly. Instead of the electric or gas heat that a regular oven uses, a microwave heats with electromagnetic radiation.
While the heat of a regular oven (or a small toaster oven) surrounds your food and cooks it from the outside, with the heat working its way in, a microwave's radiation cooks most food from the inside out. Its radiation, or waves, penetrate the food and heat up any moisture inside it. These waves are themselves called microwaves because they're short (and micro- means "small"), similar to radio waves.