A microphone hands software one number per sample: air pressure over time. The FFT converts a short window of those samples into a different answer: how much energy sits at each frequency right now. That conversion is what lets visuals respond to bass separately from cymbals.
The transform is Fourier’s 19th-century mathematics made cheap by the 1965 Cooley-Tukey algorithm, which turned an impractical computation into one that runs thousands of times per second on anything.
Practical tradeoffs live in the window size: more samples give finer frequency detail but blur timing, fewer give snappy timing but coarse frequency resolution. Every analyzer, including the one inside Photism, is a position taken on that tradeoff.