What is a “Trojan Horse” program?

Like the Greek myth, a Trojan horse is a malware program hiding inside another program that does something useful.  This could be a freeware program, like an MP3 encoder, a tool for breaking DVD copy protection or a game.  Whatever it is, when you install it on your system it also installs a “payload”—one or more malware programs such as a keylogger or a backdoor.  (See also, What is spyware and malware?)