So the first part (left half) we have two channels (stereo) each with two filtering amps.  Those take an audio jack as an input, and send the output to a switch and then thru a pot.  Then we have a second set of amps, with no filtering, that look to be set up as straight amps.  These take an audio jack as an input, but send them thru a pot first, and then the output is a jack... so basically the first part is generating your negative signal from your noise (which comes from a microphone), with a pot for adjusting the amount of cancellation.  Second part takes that, adds it to the volume-adjustable audio input and power outputs it to the headphones... 
See, program managers can read circuit diagrams. 
