An applet is a small program that runs in the context of a larger program on a client computer. Nowadays this usually refers to Java applets, which run in a browser, though it is possible the introduction of the term in AppleScript in 1993 slightly predated this usage. A similar program on a server is called a servlet.
Macromedia Flash is another widespread applet nowadays that provides motion graphics, interaction and sound.
Applets generally have the capability of interacting with and/or influencing their host program, although they are generally not required to do so.