Applets are Java programs that can be embedded in HTML pages and run in web browsers. An applet's lifecycle involves several method calls: init() is called once to initialize variables; start() restarts the applet after being stopped or loads it initially; paint() redraws the applet's output; stop() suspends threads when the applet is no longer visible; and destroy() removes the applet from memory, freeing resources. Applets allow making websites more dynamic but require the Java plugin and have security restrictions compared to standalone applications.