A computer program that appears to have a useful function, but also has a hidden and potentially malicious function that evades security mechanisms, sometimes by exploiting legitimate authorizations of a system entity that invokes the program.

Like the legendary Trojan horses in Greek mythology, a computer Trojan horse also disguises itself as a benign and often useful software that a user would like to download and benefit from. Unfortunately, doing so can actually cause great harm to their machine once installed.

Often the delivery comes by way of deceiving the receiver into opening a file that is from a trusted source, but, is in fact, intended to cause harm. This is known as a phishing attack.

Once the trojan is installed on a machine, similar to a virus, the results can vary.

Like viruses, there are some trojans that cause more harm than others. They vary from being mildly annoying, such as inserting pop-ups to your screen every hour, to more sinister and malicious in their intentions and actions such as deleting your entire hard drive. Either way, being infected by a trojan is definitely something that is best avoided.
On the plus side however, unlike viruses and worms, trojans do not reproduce by infecting other files, nor do they self-replicate.