It's your Personal Messages inbox. While it's full, no-one can send you any more PMs. Go into your Personal Messages (click on the link at the top of the page that says 'you have 123 messages, 0 are new' and it will bring up the list of messages in your inbox. At the right-hand end of each message title, there is a check box. Click on the box to put a tick against the messages you want to delete then go down to the bottom of the list and click the delete button.
