An applet can connect to a DB that's running on the same server where the applet was served from; if the DB is on some other server, then the applet can't connect to it (unless it is signed, but I suggest we leave out that possibility for now).
A workaround to this security restriction is to have the applet connect to an active server-side component on the server where the applet was served from (this would act as a proxy server, and could be a
servlet, or PHP script, or some such - probably what your friend referred to as "server script"). This server-side code would then access the DB (which could be on any server, since the code wouldn't be subject to security restrictions).
This is a whole different kind of setup and programming environment (and learning curve) than applets - are you prepared for that? If so, start reading up on servlets or PHP or some such technology, and -if you have questions about it- start a new topic in an appropriate forum. (In other words, not in this Applet forum right here).