If you want to back up the message folders locally (in addition to keeping them on the server), you can automatically move or delete older items with AutoArchive or export the items to a .pst file that you can restore later as needed and use by importing.

Step 1 - Open Outlook and click on file.

Step 2 - Select Open&Export and click Import /Export.

Step 3 - Click Export to File then Outlook Data File (.pst)

Step 4 - Select the mail folders to back up and select Next.

Step 4 - Choose the location to save the backup and click finish.

TIP: The messages that you keep in a .pst file are no different from other messages. You can forward, reply, or search through the stored messages as you do with other messages.