Comment by SJC_Hacker

The simple explanation: Lets say you have a one-dimensional time-domain signal, e.g. an audio signal measured by a microphone, which measures the displacement of air vs. time at a fixed point (assuming you dont move the microphone I guess)

The Fourier transform (of which the FFT is a discrete version of) decomposes that 1D time-domain signal (e.g. an audio signal, time vs. displacement) into frequency vs. magnitude and phase components

The frequency is basically the pitch. So for a pure sine wave, or pure tone - which sounds like those "off air" TV signals we used to get late at night back in the day. You get a bunch of zeros and a single "spike" at the frequency of the tone. The larger the amplitude of the signal, the larger the magnitude of the spike will be. As the pitch (frequency) increases/decreases, the location of this spike moves up/down along horizontal axis

The phase is basically the time offset of the signal. A tone which was delayed somehow will show up as a different phase. Note this is a relative measure - not absolute. So you won't be able to tell if the signal was offset by 1s or 2s, etc. because it has units of radians(angle), which have to "reset" as the angle wraps around the circle.

So for one signal (time vs. amplitude), you actually get two pieces of information (frequency vs. magnitude/phase)

However if you understand imaginary numbers/complex variables, those two signals are really just the magnitude and argument of FFT output, which produces a complex function