Applets are Java programs that run in web browsers. They are embedded in web pages and run on the client side. When an applet starts, the init(), start(), and paint() methods are called sequentially. When it terminates, the stop() and destroy() methods are called. Applets do not use a main method but are instead automatically called. They allow moving work from the server to the client and are cross-platform, but require the Java plugin and may not run on all browsers.