This is common, and simply indicates that the local Microsoft Outlook copy of your Google Apps for Business email is limited to a certain amount - by default this is 1GB. It does not mean that your account will stop receiving email. This only affects how much email is downloaded/synchronized with Outlook on your computer. You can change this setting to "Unlimited" or several other data amounts by following the directions here:
My Google Apps Outlook Sync Tool is telling me my "Local mailbox is full"
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