The cloud library automatically keeps your Public and Private items synced with the cloud. Although all your items are store locally as well, any change to them will automatically by send to their cloud version. This secures your items from being lost if you would somehow loose your phone and avoids the hassle of manually re-uploading small changes.
It also allows you to work on multiple devices, as new or changes items will automatically be downloaded as well.
Whenever the library is synchronizing your items, it will show you a sync bar with information about it's current progress. Keep in mind that synchronization happens in the background, so you don't have to keep the library open untill it is finished.
You can trigger a re-sync using the Force Library Resync option in the overflow menu of the app bar.
If a full resync is manually or automatically triggered and you are currently not on Wi-Fi, the sync bar will ask you if you would like to sync anyway. To do so, tap the sync bar.
If you would like to bypass this behavior and allow re-sync at any time. Go to Setting .. Cloud library .. and disable the option Full synchronization requires Wi-Fi.