This is harder than I thought lol
To me, a Supercar is not the most prestige label that can be given to a car. The word Hypercar (used by Clarkson) is the most prestige label that can be given to a car imo. A hypercar has the properties of a Supercar, but better
e.g A Supercar can do 205 mph, a Hypercar can do 220mph.
But back on topic, I think a Supercar has to look special and turn heads when it drives past like a Lamborghini or a Zonda, not like an 800bhp Nissan Skyline. It has to have unique styling, and have things on it the normal cars don't have.
Performance wise, I think a Supercar must be able to reach 200mph, be able to handle itself on a track and amaze the owner every time he drives it. As Diablo says, a Supercar is a machine that only the very privileged can own.
Also, it should be made with passion so when you drive it, it feels like your in something unique, something very very special.