Java applets are used for embedding Java applications in web pages. You should create an applet if, and only if, you are intending to do that — to provide your users a GUI written in Java which requires them to have a JRE installed on their computer.
From your other descriptions, it sounds like you are supposed to be making a web app — the game logic resides on your web server, and the interface is implemented in HTML and JavaScript. There are no applets involved here. This generally results in a more widely compatible and faster-loading interface. However, the HTTP request/response model means that it is more complex to build simple interactive interfaces robustly.
Personally, I would recommend reading up on the architecture of web applications before attempting to write one which is a game.