Clipping is when the input level of a sound source is higher than the maximum level that can be accepted by the hardware. When this happens the tops of the wave forms get 'clipped' resulting in an increasingly distorted recording. Very small amounts of clipping may be acceptable in some cases where distortion was desired. Larger amounts are generally undesirable.
Many people consider clipping in analog recordings more desirable than in digital recordings. There are software plug-ins that emulate analog clipping.