the document fairly well explains itself how it works
there is a reference voltage on the LM324, which acts like a comparator for the voltage generated by the microphone (which is amplified), if it gets above a certain volume (voltage) it turns on the amplifiers for the headphones for a preset amount of time (based on sizes of a capacitor and a resistor connected to the 555 timer) then it shuts off until the sound goes above a certain point again.