The FFT converts a waveform (amplitude over time) into a frequency spectrum (amplitude over frequency). It is the mathematical engine behind: spectrum analyzers (visualizing frequency content), parametric EQs with real-time display, convolution reverb (applying impulse responses), and room correction measurement software.
The FFT has a fundamental trade-off between frequency resolution and time resolution: larger FFT size = more precise frequency information but less precise timing information. This is why real-time analyzers use different FFT sizes for different purposes.