Each mailbox comes with 1GB (1000MB) of space. If your mailbox is full, you will not be able to receive new emails. To see how much space you have remaining, check under Set up email on the My Subscription page.
This article explains how to avoid a full mailbox.
Load emails in Gmail
You can also manage your email using Gmail.com and the Gmail apps by loading your mailbox in a regular Gmail account. This means you can receive business emails via the same mailbox and use it to send emails. Your emails will be saved in Gmail's apps and you can access them at any time.
Need more space?