A web server is a computer that holds all of the information and the software necessary to run your website.
The term Server is matched with the term Client.
Together, the term Client/Server, describes the relationship between two sets of computer software in which one set of software, the client, makes a request for service from another set of software, the server.
When we browse the internet we have a Client/Server relationship with the web site. We use a Browser, (Internet Explorer, Firefox etc) and are the Clients, the Web Site use software that is the Server.
A second definition of the word server is also valid. The computer that runs the server software is also called a Server.
That means we have Server Software running on a Server Machine and when the Server is used to provide web sites it is called a Web Server.
More reading on Web Server: Wikipedia Web Server
More reading on Client/server: Wikipedia Client/Server