At the most basic level, a web server is simply a computer program that dispenses web pages as they are requested. The machine the program runs on is usually also called a server, and the two references are interchangeable in everyday conversation. When someone enters an address into an internet browser(such as Microsoft Internet Explorer, Mozilla Firefox, or Google Chrome), the browser sends a request off into the internet asking to view the web page found at that address. The web server is the program or machine that responds to that request, and delivers the content of the page back to the user.
This can be done because every computer or device that connects to the internet has a uniquely identifying number, called an Internet Protocol address (aka IP address). This address is what allows computers to find one another and communicate across the network.
Web servers can sometimes be slowed down by things like inadequate resources on the machine they run on, or an overwhelming number of requests being received in too short a time, but generally the whole process happens so quickly it's hardly even noticeable as users navigate from page to page. The data being transferred back and forth during these exchanges must conform to a specific protocol, called Hypertext Transfer Protocol (aka HTTP), to ensure that all web pages and servers communicate with one another efficiently and without error.