A Completion Upgrade is an Item which allows you to Upgrade your buildings to a Lvl. 10.

You can only use it on a building that is level 9. there are no shortcuts.

These can be won through Lilith's Luck or bought by Rubies.

Without these, your buildings will be stuck on Lvl. 9.

Also, Some things are not available to you until you use a upgrage. For instance, you need a Lv. 10 Barracks with your outpost's to start the training of Alchemest and Reapers.