You know this one. The Internet is a worldwide network of computers that relay information to each other. Originally, the users were academics, so there’s a lot of academic DNA in its makeup (more on that soon).
The World Wide Web (where we get the now-rarely-seen “www” prefix) is the part of the Internet that you can access through a Graphic User Interface (GUI) – or in English, the stuff you can get to through a Web browser. There’s a lot of data on the Internet that isn’t accessible from the Web.