An FFT chops the spectrum into equal slices and reports energy per slice; each slice is a bin. A 2048-point FFT at a 48 kHz sample rate yields 1024 usable bins about 23 Hz wide.
The equal width is the practical catch. Human hearing is roughly logarithmic, so 23 Hz is a chasm at the bottom of the spectrum (the whole difference between a C and an E of a bass line can live in two bins) and invisibly fine detail at the top. Visualizers therefore regroup bins into perceptual bands before mapping anything to motion.
When an analyzer looks smooth at the top and chunky at the bottom, bin width is what you are seeing.