A supercell is a thunderstorm with a persistent rotating updraft. That single property, the mesocyclone, is what separates it from every other storm on the radar.
Rotation starts horizontal. Shear creates a spinning tube of air lying on its side, and the updraft tilts it vertical. Now the storm has a mesocyclone and can sustain itself for hours.
The rear-flank downdraft wraps around the mesocyclone and is where tornadogenesis usually happens, when the wrapping air is not too cold to be lifted.
Structure is visible from the outside: a striated updraft base, a wall cloud under the rain-free area, and an anvil with a hard overshooting top. If you can see all three, you are looking at a supercell and you should be somewhere else.