Expanding on what Mike said, the clutch is the leverage that temporily disconnects the engine from the transmission. The "throw-out bearing" is one of four critical components. When you depress the clutch pedal, a fork engages the throw out bearing and separates the clutch face from the flywheel allowing you to shift gears without grinding gears.

If you slip the clutch, you are not completely separating the clutch plate from flywheel contact. Do it often and long and you create a lot of heat from the slight friction between flywheel and clutch. You will burn the clutch, ie, polish it smooth, along with damaging the flywheel surface.

If you were engaging the clutch and shifting to neutral, you can safely let out the clutch. Slowing without shifting to neutral while reving the engine with foot on brake, will cause more problems with brakes than clutch.

You will know about problems before they become serious as the throw out bearing will make noise and you will have trouble shifting. Slipping the clutch causes heat buildup and burning of the clutch. You will smell it much like you can smell overheated brakes.