I'm having an ongoing discussion with Microsoft about this exact problem.
It's definitely NOT an Apple folder. This can be proved if you try to create a folder called "Files" as a new root folder using Outlook 2016. The error comes back that this folder already exists, even though it's not shown.
The problem is more likely a new feature that MS have added that helps with searching content as the "Files" folder contains searchable content of all the attachments from all your emails. The Files folder is marked as a "Distinguished" folder, meaning it
has special significance (i.e. it's a system folder) and cannot be deleted, a it like the "Junk", "Clutter" and "Sent" folders.
See here for details:
https://msdn.microsoft.com/en-us/library/jj191225(v=exchg.150).aspx
I'd like to see the "Files" folder made hidden like the other Distinguished folders that Apple Mail doesn't show, e.g. the "Conversation Action Settings" folder is hidden.
My gut instinct tells me that the "Files" folder is missing some attribute that Apple uses to hide it from the normal folder listing and it would be easy for MS to add such an attribute so that it's handled like the "Conversation Action Settings" folder.
Any update from MS or the community greatly appreciated!