The Fast Fourier Transform (FFT) is a collection of techniques that exploits symmetries in the Discrete Fourier Transform (DFT) calculation to significantly reduce the computational complexity from O(N^2) to O(NlogN). It divides the DFT calculation into smaller pieces by splitting the input sequence into even and odd parts, recursively applying this splitting to obtain a reduction in computation time. A graphical representation shows how the direct DFT calculation becomes more efficient using the FFT approach.