We've seen several Mac users running Outlook who have gotten activation failures this morning. Apparently there's an issue on Microsoft's end. In the meantime, we've found that having the user quit all Office apps, then going in the Office 365 Portal and deactivating their Office install on that computer, then having them re-open Outlook resolves the issue.
We experienced this as well,
When we see activation issues, we sometimes run the Microsoft License Reset Tool: https://go.microsoft.com/fwlink/?linkid=849815
But can see that upgrades as of now do not need this and are working.