The waveform is the most fundamental representation of audio. At the macro level, it shows the overall structure — loud and quiet sections, fades, and edits. At the micro level (zoomed in to individual samples), it reveals: transient shapes, DC offset, clipping (flat tops), and zero-crossing points (where the wave crosses the center line — ideal edit points).
Editing at zero-crossings prevents clicks and pops when cutting audio. The waveform is also used for phase/polarity checking: a kick drum waveform should start with a positive (upward) excursion. If it starts negative, the polarity is inverted — which can cause cancellation when combined with other mics.