If you want to free up space in your mailbox but don't want to delete the emails, you can save them to a hard drive or cloud storage.

Simply go to your settings in your mailbox,  select import/export from the menu and from there you scan select the folder you'd like to archive, select the date range that you want to archive and then click on export as EML. The zip file links will be emailed and you can download the emails from the link within the next 30 days after creation and save the zip file to a hard drive or cloud storage.