Essentially, the World Wide Web (WWW) is made up of a lot of interconnected computers (via phone lines, cables, or satellites). Some of these computers are designed to serve out webpages. These computers are called web servers, which are usually running 24/7. Other computers, like the one you are using to read this text, are called clients. Client computers make requests to server computers, like asking for a web page and its associated graphics. The server computer responds by feeding (or serving) the web page data back to the client.
The Internet is often confused with the World Wide Web. The Internet consists of a wide range of technologies including email, file data transfer, protocols (communications infrastructure) as well as the Web. The World Wide Web is just one component of the Internet.