Burning the Clutch"Burning the clutch" can mean multiple things, but in common terms, burning the clutch is wearing down the clutch. It does not actually catch on fire.
Wearing down the clutch is the aftermath of increased pressure and heat on the clutch plate, which files or shaves down the plate making it glass-like and smooth. Since a clutch works by creating friction between the grooves of the two plates pressing together, a smooth plate changes the kinetic energy the clutch produces.
This can happen due to "riding" the clutch, meaning the vehicle driver rides with his foot on the clutch and weakens the springs on the pedal, which alters the performance of the clutch.