When you buy a new pair these days, pressing that button causes the headphones to say "Configure the action button in the Bose Connect App"

Not on the first gen, however, I had no use for the app and deleted it after the first time I played with it. My plan was to download the app whenever I wanted to do something, then immediately delete.

By default the button is set to use voice controls with your phone. The app let's you make it do anc controls