First, ensure that you’re able to see folders that are “On My Computer”.
In Outlook, go to the Outlook/Preferences/General. Be sure that “Hide On My Computer folders” is unchecked, then close the Preferences window.
Next, create a folder in which you’d like to move your important emails to. Select the folder in which you’d like your new folder to appear, then File/New/Folder. A new folder, by the name of Untitled Folder, will appear, ready to be renamed. Name the folder appropriately, then press Return.
Select the messages you’d like to move to the new folder (you can use Shift/click to select a bunch of messages), and right-click on any selected message. From the resultant menu, choose Move, then your desired destination.
*If your intent is to free up space in your Commonwealth mailbox, make sure you are NOT dragging and dropping messages. If you drag and drop the messages (instead of right-clicking and selecting Move), it will copy the messages, leaving them in your Commonwealth mailbox as well as your On My Computer folder, and you will need to go back and delete the original messages from your Commonwealth mailbox.
Auto-archiving is not available on Outlook for Mac. However, if you'd like to automate part of the process, you can set up a rule in Outlook/Preferences/Rules to move messages of a certain criteria to a selected folder (see screen grab below for an example of a rule based on Date Received), and you can manually move messages from that folder to your On My Computer folder periodically (as opposed to searching through your mailbox for messages to archive).