Distortion is one of the most frequently heard effects in music. It is applied to almost every guitar sound in rock and metal and can be just the thing needed to spice up a sound. So let's start basic and look at what distortion is.
A sound wave can be looked at in a very simplistic term, a wave of pressure, moving through air. In real life, it looks very much like this:
See the forward moving wave of pressure as the slinky bunches up? That is very similar to how sound moves. However when we transform sound into electricity, e.g. in a recording, it is easier to visualise like this:
Where the voltage of the electrical signal is proportional to the amplitude (pressure) of the wave. The higher the wave in the slinky, the louder the sound would be.
So imagine we are in a room with a high ceiling, we have a lot of room for the slinky to move. if we put more energy into the waves, it will go higher. An amplifier or similar piece of audio equipment can be seen like a room with a slinky. If you put more energy into the slinky, the waves will be bigger, very much like when you turn the gain up on an audio signal and it gets louder.
But there is a physical limit, in the room analogy, it would be the ceiling. If we were to put enough energy in, that the slinky would hit the ceiling, the slinky would stop conforming to the sine wave shape. Every bit of slinky that would have gone above the ceiling is now briefly lying flat against it, in a similar way to the red line in the image below:
This makes it more like a square wave, and with some basic understanding of waves, it can be supposed that it will sound harsher, with more upper harmonic content. it also means that any data or variation in the wave that is at a point louder than the ceiling, is lost too. Look at the pink line in the diagram below:
Above the red line, the wave could be doing any manner of sounds and the listener would not be able to tell as the data is lost. Even thought the blue line and the pink line would result in very different sounds, the only line audible would be the red one.
This is why it's always so important when recording, whether its a band, interview or film, to have the gain at an appropriate level. Once there is distortion, that data is gone. Even if you turn the volume down after the amp, the data is lost. Forever.
If you are a guitarist or other musician and are applying this effect deliberately, then it is brilliant but it is those few that do it by mistake that will have all the regret and will possibly have to start from scratch.