"Slipping the clutch" refers to a technique where the clutch plate only partially engages the flywheel. The reason this is done is to allow the engine to operate at a rev range that provides greater power than the rotational speed of the output shaft would allow given a particular drive gear. The net effect is to reduce the instantaneous power transferred to the drive wheels without causing the engine to stall.

Because of the speed mismatch between the flywheel and the output shaft, this technique will wear down the components of the clutch/flywheel faster.

If you're still confused, consider the situation where you are stopped at a red light on a steep hill. Once the light turns green, "slipping the clutch" is often done to prevent the car from rolling backwards, yet still provide enough forward motion without accelerating wildly into the car in front of you.