A Trojan Horse is a type of software that seems useful (e.g.: a game or antivirus) and encourages the user to install it. Once it's installed, though it can be malicious without the user knowing.
This comes form the Ancient Greek times when the Greeks sent a large wooden Trojan Horse then pretended to sail away in boats, as if the Greeks were retreating. The Trojan people brought it into their town as a trophy of victory, but at night, Greek soldiers who were hiding inside the horse sneaked out of the horse and opened the gates of the city to let the other Greeks who 'sailed away' in and in the end, they took the city of Troy, making the Greeks win the war.