Microsoft Outlook allows you to archive (copy) messages that are stored on the mail server into an archive mailbox on your local computer. This is a great way to keep you from going over your storage space quota and keep mail that is important to you for an indefinite time. 

You can archive your emails in single click. Instructions are found in this Microsoft article Archive messages in Outlook for Mac.

Note: Some versions of Outlook will allow you to auto-archive mail, but Outlook 2016 for Mac does not have this function. You can archive your mail by setting up Rules to manage your archive based on specific criteria. Instructions for doing this are found in this article Create Rules in Outlook 2016 for Mac.