By default faculty and staff have a size limit on their mailbox of 100GB. After you reach the size limit, you will no longer be able to send emails. This FAQ details how to check the size of your mailbox in Outlook on a computer running Windows.
Select Tools next to Mailbox Settings:
If your mailbox is approaching 100GB, it's a good idea to start online archiving to clean up some space. Here are instructions on how to set up online archiving using OWA.