Applets consist of compiled Java code that are downloaded to a browser when the appropriate link is included in the HTML page. They allow a full range of Java to be executed, but are generally limited to Java version 1.1. They are secure in that the applets are not allowed to read or write files on the browser client machine and are restricted in other ways also.
Here is Sun's tutorial on applets.
Here's the location of Dori Smith's applets which we will be using extensively in the course. (You may also wish to buy her book, Java for the World Wide Web : Visual Quickstart Guide.)
Here's Sun's java.awt.Graphics API for 1.1. This is all you need in the way of graphics primitives for your graphics programming for now. Additional capabilities can be found in various examples, such as Smith's.