Well, the first and main reason to use a distortion pedal is because, obviously, it just sounds really amazing. While altering the original signal may look like a nasty thing to do to a purist, it actually allows guitarists to create their own signature sounds and add a crunchiness and warmth that wouldn’t be possible otherwise.
Distortion compresses the audio signal, resulting in a specific dirty or fuzzy timbre that may suit a particular music genre. You can get the growl of Stevie Ray Vaughan, opt for the smooth overdrive of David Gilmour, or go for something with a more aggressive bite for playing hard rock or heavy metal tunes.