A piece of malware masquerading as an innocent program.
A "Trojan" is a type of computer malware requiring user intervention to run. The idea behind a Trojan is to pose the malware as a piece of software the user might want to install, and when the user runs the program the virus is released. Often the disguise program will function as the user would expect, to prevent arousal of suspicions.
The term "Trojan" comes from the story of the Trojan Horse, a classic tale in which the Greeks hid inside a large wooden horse left outside the gates of Troy. The Trojans took the horse past the gates, and at night the Greeks took Troy from the inside.