YouTube has provided some more details on how its upcoming offline viewing mode will work: if you add a video to your device to view later, and then disconnect that device from the Internet, you'll be able to watch that video for up to 48 hours without Internet connectivity.
Once those 48 hours are up, you'll need to reconnect to the Internet if you want to watch the videos again, it will refresh that you're connected, and the videos will still be playable, for another 48 hours. The offline videos and playlists will be stored on your device, under an "on device" section of the YouTube sidebar. You can add more content to your device directly from the watch page, or from wherever you are viewing a video from.
Google will push out an update of YouTube for mobile in the coming weeks, where this new feature will be front and center.