If you want to create a backup of your email data you can follow this guide to do it.
When you export data from Outlook, the original items are copied to the export file, but are not removed from the current folder. You can export to many different file types, including PST files and delimited text files.
Export data in Outlook 2013
Note: To be extra safe and to ensure the local .pst file is not corrupted, it is recommended to perform this task while using Outlook in Web Access, to ensure that the actual data from the server is being exported.
For importing your data files see How to Import Data in Outlook 2013.