When the shape of a waveform or other varying voltage has been changed, technically it has been distorted. When people say they hear distortion, they are often referring to an audio waveform that has been “clipped” (the top and bottom excursions get flattened out when the reach a certain limit) or when it has “entered saturation” – it is being bent because it is getting close to clipping. Sometimes you will hear users talk about “overdriving” a module, which causes distortion. Distorting a waveform alters its harmonic structure, often adding higher harmonics.
You will also hear distortion used when a waveform is changed for purposes other than just overdriving it. Phase Distortion Synthesis is an example of this. Indeed, any waveshaping technically is a form of distortion.