The applets came out in the first versions of java alla for 1995 and 1998 but since they were running as browser plugins they had big security problems, even their way of programming was a security problem, because they allowed the code of the programmer to do anything on the client machine, even format the machine (obvious with the necessary knowledge).
That is why the servlets appeared and then the JSPs. Many programmers began to use the applets only to install dll necessary for their code. But given the problems of having access to the client machine and that servlets and jsps already existed on the server side, the browsers began to eliminate the plugins (including java and flash) and everything based on NPAPI technologies.
Currently the only browser that supports the java plugin is firefox, and mozilla has announced that it will be deleted by the end of 2016, it will only support flash and in the future it will also be deleted:
link
This does not mean that the browsers stop supporting the java language as I have read in some uninformed pages. The servlets and JSPs that are on the server side are still working, so they must change their applications from applets to servlets and JSPs, or to the client-side alternatives that now exist, or to the new frameworks that work on servlets and JSPs. There are many alternatives: Javascript and AJAX (with all the frameworks based on them like AngularJS, Node.js, etc), HTML5, JavaFX, Java Web Start, etc.
It is not possible that after the security problems of the applet technology were seen and the alternative came out, it would still be used almost 20 years later. You have to update yourself and you only have 2016 to do it.
Greetings