A Java applet is essentially a small non-standalone application that can be run from a web browser. Put simply, when a user accesses and runs an applet, the Web browser downloads the applet code from a Web page to the user's machine and then runs it. Since the applet is essentially a running program after it is loaded, it can do everything that a standalone Java program can do if it were run from the user's machine.
The key here is that an applet is a non-standalone application, and it is specifically run from a Web browser.