I've built a toy oscilloscope with an Arduino, acquiring the samples with the ADC and plotting the spectrum on my computer. The spectrum is the output of the FFT algorithm. You can see a video here of the program in action.
The yellow line is the actual value of each sample as the output from the Arduino's ADC. The red line is the magnitude of each complex number as the output from the FFT function, and the green plot is the angle of each of those complex numbers. The first spike is noise from the AC main power line, which is 50 Hz.
The red plot shows the "energy" of each frequency. What information does the angle shows? Is there an intuitive explanation?