You are getting this email notification because your user's mailbox is almost or already reached the available email quota. (See more info on Mailbox Getting Full Notification)

You may advice the user to clear some emails on the webmail or increase your user's email disk space.
If the user is accessing emails from POP3 email client e.g. Ms Outlook, you may advice the user to set to download-and-delete the emails.

Do ensure sufficient quota has been allocated for the user's account, especially for the more active ones– the ones that are getting constant notification on mailbox getting full.