Step 7: How does it work?
The 555 timer generates a square wave of a frequency and duty cycle determined by the potentiometers and capacitor across pins 8-7 and 7-6,2. This square wave is applied to the gate of the MOSFET turning it off and on many times a second (tens of thousands) thus allowing pulsing current through the primary coil of the flyback at a frequency generally in the 30-50khz range.
When an audio source is fed into pin 5 of the 555 chip it will actively change the duty cycle and frequency of the square wave to the sound waves of the audio source. This is audible in the arc via the changes in air pressure surrounding the arc, and as it is an audio signal altering this pressure we can hear it as sound.
If you have an oscilloscope then you can view this square-wave by connecting your scope probe to pin 3 of the 555 timer. Connect the scope probes ground clip to circuit ground.