Saying it another way, the FFT is a fast way of obtaining the fourier series of a function in the time domain. In the case of the VFX processor, the time domain function is an audio signal. The FFT is used in numerous applications from radar signal processing to brain wave analysis. The FFT does increase the speed that a computer can compute the DFT and so a realitive improvement factor is a good way to look at it. Let's look at the DFT first.
Lets start with the fundamental.
Multiply the first data point by the first point of the sine wave. Take the 2nd data point and multiply it by the 2nd point of the sine wave. Add that to the result of the first multiplication. Repeat this for the 3rd, 4th, 5th, 6th ,7th and 8th data points. The result is a measure of the amount of the fundamental wave in the signal.