Unified Messaging is a concept used in Microsoft Exchange. In the current day world we have voice mail and email. Voice mail is a message which a person leaves in case he/she is unable to get hold of the person they are trying to reach. One can access a voice mail over the phone. Emails can be accessed primarily on the desktop but can also be accessed on the phones and other devices depending on the client.
With Unified Messaging, one simply needs a single device to access emails and voice mails. So in case you set up Unified Messaging for Outlook, you could receive both emails and voice mails at the same place. It is a one stop solution, improving productivity by saving time.