Distortion
Distortion is technically any change to the waveform of a signal. The specific type of distortion we are most familiar with is clipping - where the peak amplitude of a signal exceeds the ability of an amplifier to reproduce it accurately. The peaks are compressed - visually, this gives the appearance that they have been clipped off.
Clipping can be desirable for certain instruments or for a whole song. Many devices and pieces of software have been created to provide such "musical" distortion. Guitar is a primary instrument that makes use of distortion, often preferring the soft-clipping of vacuum tubes over the hard-clipping of silicon-based amplifiers.
However, not all clipping is desirable, often the result of poor gain staging. This may result in crackles, static sound in the signal, reduced clarity, and decreased signal-to-noise ratio.