Supercells are formed when the wind at the surface of the earth is going in the opposite direction of the wind at an altitude of roughly 20,000 feet, and there is a large difference in speed between the wind. This creates what is called the mesocyclone. The mesocyclone is the rotating updraft that forms the center of a supercell. By rotating updraft, we just mean a big column of air which spins around and goes up. This big column of spinning air is what creates all the severe weather that is caused by a supercell.

At first I thought of super animal or plant cells, or super battery-type cells, but in google I learned that supercells are a kind of thunderstorm that rotates around and around, because it has a kind of cyclone in it. Here's a link to wikipedia: supercells.

Supercells are very structured storms whose distinguishing feature is an updraft that rotates around a vertical axis. Updrafts occur warm, moist air is pushed up by cooler air. This leads to formation of a storm, but not necessarily a supercell. As the moisture in the air condenses and falls as rain, it forms a downdraft which cools the air of the updraft and eventually stops the updraft. If a shearing wind causes the updraft to rotate though, then the downdraft no longer cools the updraft and the supply of moist air is not choked off. Thus to form a supercell the important ingredients are a body of warm moist air running into a body of cooler air coupled with winds that cause rotation with increases in altitude.

I assume you are referring to supercell thunderstorms, and not some other meaning of the phrase.

Supercell thunderstorms are defined by having a persistent, rotating updraft. Generally, to cause these, you need wind shear (winds at low altitudes are blowing at a different speed or in a different direction than winds higher up), as well as the ability to extract energy from the air by condensing water. Supercells can happen on their own in the right conditions, or they can be part of larger storm complexes. Notably, hurricanes provide the wind shear on their own, and supercells embedded within the eyewalls of hurricanes are an active area of research (particularly because the tornadoes that these hurricane-embedded supercells produce are a big part of why hurricanes are so destructive).