Why are some computer viruses called Trojans?

Hidden malicious programs (most are not viruses) are called "Trojans" from the story of the Trojan Horse, from the war between Greece and the city of Troy, as written in Virgil's Aeneidand referenced in Homer's The Odyssey. The trojan horse was a threat masquerading as a gift. Similarly, trojan programs seem innocuous, but are designed to damage your computer or use it for harmful purposes.

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In the Trojan War, one side was the Greeks and the other was the people from Troy. They were fighting for this beautiful queen, Helen, wife of Menelaus. Eventually the Greeks saw that the Trojans were winning the war, so they devised a very clever plan: they would create a giant wooden horse (because the Trojans worshiped horses) and then leave it behind as they left, pretending to give up. The wooden horse would be a peace offering. The Trojans accepted it, took it into the city walls, and then they partied at night and got drunk. After the Trojans were sleeping, Greek soldiers hiding inside the hollow wooden horse got out and opened the city gates of Troy to let their much larger army inside. Because the Trojans were caught off guard and drunk, they had no choice but to surrender and the Greeks won the war.

Trojan Horse programs work in the same way. They disguise themselves as legitimate programs or files. When you accept to download them, they infect your computer and run malicious processes in the background without you knowing. They often really do have the program that you intended to download, but they also come with a virus or something else to corrupt your computer. Hence the name, Trojan Horse or Trojan.