This course will answer that question. What is a server? A very simple definition is a network device that provides services. The next question is what is a service? A service is something running on a device that provides resources to other network devices. Here are a few examples of services you server can provide.
Many versions of Windows are missing from the table above. The versions above cover the versions of Windows based on Windows NT. Windows NT was a big improvement on versions of Window based on Windows 3 and Windows 95. Windows NT was a rewrite of Windows from scratch, to include a new infrastructure and maintain application compatibility with a goal on portability. If you are interested in reading more about the creation of Windows NT this book is a great resource.
Windows Server 2012 R2 comes in different versions.
In the files section of this page there is a PDF document from Microsoft that outlines the differences between the different versions of Windows Server 2012 R2.
Windows Server 2012 R2 has two different ways it can install. You can do a Server Core Installation, or do a Full Installation. Server Core is a mode of running Windows Server 2012 with only a command prompt. Running the server this way will conserve hardware resources, reduce disk space usage, reduce patch frequency and reduce attacks.
Server Core was introduced in Windows Server 2008. When you installed Server Core you could not switch to a Full Installation. Many administrators kept the Full Installation because it's easier to use a graphical interface to set things up. Microsoft has done a few things to make it easier to use Core Server in Windows Server 2012. Introduced with Windows Server 2012 is the ability to switch between a Full Installation and Server Core. This allowed administrators to set up the server using the graphical tools they were used to, then switch to Server Core giving them the benefits of Server Core. In Windows Server 2012 R2 the new Server Manager application allows you to remotely work on your servers using graphical interface even if the remote server is running Server Core. Using Server Manager, you could setup your server and never touch it again, by doing everything remotely using your workstation. And finally they upgraded PowerShell to Version 4 which introduces many new cmdlets greatly increasing the power of the shell.
A clean install of Windows Server 2012 R2 doesn't do very much. In order to start providing services to your clients you need to install Roles. In Windows Server 2003 R2 and earlier the server had a lot of capabilities installed waiting for you to activate and use them. Anything that wasn't there by default could be added using the Add / Remove Windows Components wizard. In Windows Server 2008 the idea of Roles and Features was introduced. The idea was nothing extra is installed unless you ask for it.
When you setup a server you have a plan for it. The server will hold data, or provide printers, or authenticate people. After you install server you can install the desired Role, then follow the steps to configure if needed. Features add capabilities to Roles. A good way to remember the difference would be a Role provides services to network clients, and Features provide capabilities to Roles.