In simple terms, a server is a computer that provides a service to other computers (known as clients). Many of the new & high end functionalities of Office 2013 become available when they interact with Microsoft Server software. Products such Microsoft Lync Server provides unified messaging on the desktop. Think of it as Skype on steroids, with the ability to communicate via instant message, voice call or even video conference call, all from the one simple interface.
Microsoft SQL Server gives the database functionality used by many enterprises. The Server houses the powerful database software, & client computers can update or access that information at any time, sharing information simultaneously when necessary.
Microsoft Exchange Server adds many powerful features to your existing Outlook interface. With Exchange, you can now see other staff in your Outlook calendar & contacts. You can invite people to meetings, book resources, & check when they are available for appointments. Shared contact folders allow you a common address book that every staff member can access & update.
Microsoft Sharepoint Server provides an intranet, effectively an internal website that can house all sorts of information for your organizations internal use. Policy documents, reports, leave forms, rosters, anything you like can be located on your own intranet.