Language, device name, firmware updates, voice-prompts, auto-off-timer, list of paired devices, multi-headset-mode, and so on. The app is almost mandatory, especially since iOS pushes you to download it on connect.
Interesting. I have QC35s but have never downloaded the app, although I have Android so I'm not sure how pushy iOS is. I've been able to use the headphones regularly without the App. The features you mention don't seem that important to me.
I've also never downloaded the app and, in fact, didn't even know it existed. I've never been notified about it in any fashion on iOS?
It isn't obvious, but the mention of the app is on the inner flap of the packaging
I have these headphones paired to a number of devices and the app makes managing that simpler (if, say, I want to prioritize the output from my phone instead of my laptop).