Amplitude is how far the waveform swings from zero: bigger swing, more energy, more perceived loudness. It is the simplest thing to measure about a signal and the first thing every reactive system measures.
The subtlety is that instantaneous amplitude flickers thousands of times per second, far too fast to drive anything visual directly. Useful systems summarize it, either as peak (the largest recent swing) or as RMS (the recent average energy), and the two disagree in informative ways on punchy material.
Perceived loudness tracks amplitude logarithmically, which is why level is expressed in decibels and why linear amplitude mapped straight onto visual size reads as strangely lifeless.