A Trojan (also called a Trojan horse) is.....

A software program in which harmful or malicious code is contained within another (seemingly harmless) program. When this program executes, the Trojan performs a specific set of actions, usually working toward the goal of allowing itself to persist on the target system. Trojans can allow hackers to open backdoors on your system, giving them access to your files and even network connectivity.

It "is a piece of unauthorized code hidden within a legitimate program (101)." Trojans can carry viruses and other programs that may damage your computer once you run the program that the trojan is hidden in. Trojan horses may be either simple batch files or code containing redirected escape sequences intercepted by the ANSI.SYS driver.