Remember, if you want to delete a message, just click the checkbox next to the message you want to delete and click the blue "Delete" button.
One thing to keep in mind is that as you delete messages, you are actually sending them to the "Trash" message box.
These messages, however, are not permanently deleted until you also delete the messages from the "Trash" message box.
Once you have sent a message, your message becomes a "Sent Item." Sent messages are automatically saved in the "Sent Items" message box found within the Message Center, until you delete them.