Clipping may be described as hard, in cases where the signal is strictly limited at the threshold, producing a flat cutoff; or it may be described as soft, in cases where the clipped signal continues to follow the original at a reduced gain.
Clipping is preferable to the alternative in digital systems — wrapping — which occurs if the digital hardware is allowed to "overflow", ignoring the most significant bits of the magnitude, and sometimes even the sign of the sample value, resulting in gross distortion of the signal.
Clipping can be detected by viewing the signal (on an oscilloscope, for example), and observing that the tops and bottoms of waves aren't smooth anymore.
When clipping occurs, part of the original signal is lost, so perfect restoration is impossible.
However, when repair is the only option, the goal is to make up a plausible replacement for the clipped part of the signal.