General amps seek to diminish distortion. In particular:
1. Clipping - an overly amplified signal can have the peaks of its signal "clipped" off.
2. Cross-over distortion - because of the way most amplifiers work, one part of the circuit amplifies the positive signal, and one the negative (above and below the midpoint of the signal). Where the one part "crosses over" you can get a misalignment which results in distortion.
3. Harmonic distortion - for example the extent to which a 400Hz tone is translated into a certain amount of 800Hz, 1600Hz etc overtones.
All of these things can actually result in a cool guitar sound in the right proportions. Hard rock in particular has strongly distorted sounds created by tube amps (for the most part). But even sounds which we think of as cleaner have a significant amount of tube distortion (e.g. the intro to Sweet Home Alabama, or the main riff of Day Tripper). If you put an electric guitar into a regular amplifier, in general, it sounds flat and terrible.