A ballast is a piece of electrical equipment that transforms the electricity from the household Mains socket to supply one or more lamps, usually fluorescent tubes, to light an aquarium.
These units come in two type : Electronic and Mechanical.
These are power efficient, run cooler, more reliable operation, last longer but usually cost a little more.
These are the orignal lighting units, they use a lot of power to run (often 50% of the lights they run) so they run hot as a result, contain a Starter unit which requires changing, are physical larger than the electronic ballasts. But are often cheaper.