It's client side code. You download a class file or an archive of them, you go to the site with the applet tag and your browser invokes the client side code. It runs in the java virtual machine on your computer.
The point is: the fact that you need a runtime environment means that you are executing code locally, which in general web terms, is a bad idea.
I'm sure everything is kosher with it, but it could all have been done server side and never require a download at all.