When the guitar signal is pushed too hard, the amplifier's output transistors begin to clip, which creates a harsh and distorted sound. The amount of distortion can be controlled by the amount of gain that is applied, and by the type of overdrive or distortion pedal that is used.
Guitar break up can be used to create a variety of different sounds, from a mild overdrive to a full-on distortion. It is often used in rock and blues music, but can also be found in other genres such as jazz and country.
Some guitarists prefer the sound of natural amplifier break up, while others prefer to use overdrive or distortion pedals. There are pros and cons to both approaches.
Natural amplifier break up can sound more natural and organic, but it can also be more difficult to control. Pedals can provide a more consistent and predictable sound, but they can also sound less natural.
Ultimately, the best way to decide which approach is right for you is to experiment with different amps and pedals and see what you like best.