Your Xbox One needs to phone home every 24 hours, or no gaming for you
So the Xbox One doesn't require an always-on Internet connection, but you do need to dial into the home servers every 24 hours for the system to operate. This is how Microsoft describes the limitation:
With Xbox One you can game offline for up to 24 hours on your primary console, or one hour if you are logged on to a separate console accessing your library. Offline gaming is not possible after these prescribed times until you re-establish a connection, but you can still watch live TV and enjoy Blu-ray and DVD movies.
The system is “designed to verify” your games and your system, and it will be tracking what you give to friends, if you've bought any used games, that sort of thing. It will gather this information once every 24 hours, and if you don't have an Internet connection for over 24 hours? No gaming for you. If you have a spotty Internet connection, you may need to manage when this check-in occurs, and those without Internet connections simply won't be able to play at all.
It's a brave new world, and we're not all invited to the party.