An old version of the Wikipedia page has this...

The ethereal sound was created by laboriously building up multiple overdubs of the voices of Stewart, Graham Gouldman, Godley and Creme singing a single note in unison. This multi-track was then mixed and dubbed down onto 16-track tape. This process was repeated across all 16 tracks to create a lush 256-voice "virtual" choir that could "sing" chromatic chords. A number of these prepared multi-tracks were then cut into several endless loops, each of which contained the basic notes of the main chords used in the song.

The chorus loops could then be played by using the mixing desk rather like a keyboard -- each chord could be sounded by bringing up the fader for that loop. The instrumental break featured the repeated spoken phrase, "Be quiet, big boys don't cry..." spoken by Kathy Warren, the receptionist of the Strawberry Studios where the band recorded the track. These whispered lyrics would later serve as the inspiration for the name of the 1980s band, Boys Don't Cry.

The effects that were created are really fantastic. But I just listened to it on headphones and the acoustic rhythm guitar in the background on the right channel - that's very easy to hear on headphones - is pretty damn lame.