If you are receiving errors about being close to your quota for your Exchange e-mail account, you should consider archiving your older messages. Archiving copies old e-mail messages and attachments to an Archive.olm file (you can change the name during with the manual export process) and then removes the data from the Exchange mailbox decreasing its overall size. Items moved to an Archive.olm file are still accessible by opening the file through Outlook, and should be included in regular backups to prevent lost data. If you need more assistance in managing your mailbox size, see the Quota Management page for Outlook 2011.
The Export window will appear. Select Outlook for Mac Data File (.olm) and make sure that Items of the following types: is selected (unless you have a reason to only archive a project or category).
Choose a file name that will help you identify the file later. Try Archive_Date.olm. Then, click Save.