If your mailbox is full then email will bounce back to the sender, you can increase the quota for the inbox from your cpanel control panel. Here's how:
- Login to your cPanel control panel
- Click on "Email Accounts" under the "Email" group of icons.
- Click on the "change quota" icon for the email account you need to alter the quota for.
- Amend the quota and click "change"
All done, your inbox will now have the new limit allowing new email to be delivered.