In the early days of Java, one of the critical advantages that Java applets had over Java applications was that applets could be easily deployed over the web while Java applications required a more cumbersome installation process. Additionally, since applets are downloaded from the internet, by default they have to run in a restricted security environment, called the "sandbox", to ensure they don't perform any destructive operations on the user's computer, such as reading/writing to the filesystem.
However, the introduction of Java Web Start has made it possible for Java applications to also be easily deployed over the web, as well as run in a secure environment. This means that the predominant difference between a Java applet and a Java application is that an applet runs in the context of a web browser, being typically embedded within an html page, while a Java application runs standalone, outside the browser. Thus, applets are particularly well suited for providing functions in a web page which require more interactivity or animation than HTML can provide, such as a graphical game, complex editing, or interactive data visualization. The end user is able to access the functionality without leaving the browser.
Reference:
http://java.sun.com/docs/books/tutorial/deployment/applet/
