On iPhone, there is a place in Settings to turn off "Background App Refresh." The purpose is to restrict apps from using data in the background and only be allowed access when the user is interacting with it on screen.
Earlier this year Facebook began auto-playing their videos in the News Feed by default. And once a video played, Facebook would use a Background Audio command to persistently access your data and keep itself updated. Basically this is circumventing the restriction of Background App Refresh: Off. Super dirty, and why I'm only accessing Facebook via Safari on iPhone now.
"Update: With iOS 9's improved energy consumption stats, it's easier to guess one of the various tricks Facebook may be employing to stay active in the background and drain battery. On my girlfriend's iPhone, for instance, iOS 9 reports 5 hours of on-screen usage for the last 7 days, and another 11 hours of background audio usage with Background App Refresh turned off.
My guess is that Facebook is hijacking audio sessions on iOS by keeping silent audio in the background whenever a video plays in the app. And because, by default, videos on Facebook auto-play on both Wi-Fi and Cellular and few people ever bother to turn it off, that means there's a high chance the Facebook app will always find a way to play a video, keep audio in the background, and consume energy to perform background tasks. I'm not alone in noticing the mysterious "Facebook audio" background consumption, and video auto-play seems to me the most likely explanation at this point."