Web Server

The reference of Web server could be for any of two different context. It could be a reference to the machine hosting the website or some content or the software that makes the machine host a website.
If we are refering to the machine and not the software then things like IBM, fujitsu(   ) servers would be  
an examle for the reference. If we refer to the software then things like Apache, Microsoft IIS would be some example for this reference. I would mention a few points over the software reference in the next paragraph .
The Web servers like Apache help you build your system to host a website. It is one of the contents of the package needed to host a website. The package would contain :
1.  A server OS (Windows Server, Linux)
2. A web server software ( Apache , IIS)
3. A database management system (MySql, MariaDB)
4. A scripting language ( PHP)
So what exactly does the web server do?
It handles your request. It makes sure that everyone gets what they want from the server. You send in a request using HTTP and then the server responds to it by generating a HTML file. This HTML file is sent to  you and your browser converts the markup language into a good looking thing. Note that even accesing the page is a request.So when we say apache server we mean a server hosting its operation using an apache software.

https://www.youtube.com/watch?v=fRLJ3bnbHmE, http://en.wikipedia.org/wiki/Web_server

A type of web servers are Application Servers, servers which deploy(load and allow the use of) web apps to do a certain type of work. This can include apps that facilitate the communication between the host and the client browser. They usually are servlets, EJB's, JSP etc that are coded in JEE(Java Enterprise Edition). The latest JEE is JEE 7.Few of the famous application servers are JBoss,Apache Tomcat etc.