Mailbox Full (OWA)?
Your mailbox quota has been exceeded:
If you have used up your allotted quota then you will be unable to send or receive new messages. You must clear down some existing messages.
Please try the following:
Go to the Options screen and scroll to the bottom to select Mailbox Sizes. Click on this to see which folders are using up the most space.

Now go to those folders using the most space and click on teh Size column to sort them by size. It may be better that you delete fewer, larger emails than lots of smaller ones. After deleting emails you will need to clear the "Deleted Items" folder before any space is recovered.
Emails often accumulate unnoticed in the "Deleted Items", "Drafts" and "Sent Items" folders.
If you cannot see any items in the folders check that the "Messages" pull down menu at the top of the screen is not showing "Unread Messages" If so, change this to either "Messages" or "Two Line View"