RMS squares the signal, averages it over a window, and takes the square root, producing a number that tracks sustained energy rather than momentary spikes. A snare hit and a pad chord can share a peak level while their RMS tells the truth: one is an instant, the other a wall.
Meters distinguish the two for exactly that reason, and the loudness war was fought in RMS, squeezing average level upward against fixed peaks.
For visuals, RMS is the natural driver of sustained qualities like glow, density, and camera energy, while peaks and transients drive hits. Map both to the same thing and the image stops breathing; separate them and it starts.