Java applets are small Java programs that can be embedded within HTML pages. When a user views a page containing an applet, the applet code is transferred to their system and executed by the Java Virtual Machine within their browser. Applets allow for interactive features on web pages like capturing mouse input and including buttons or checkboxes. They can also play media formats not natively supported by browsers. Applets are embedded using the applet or object tags, which can specify the applet's location and download any necessary Java plugins.