A Trojan Horse virus is named after the huge wooden structure the Greeks used to enter into the city of Troy. The horse looked innocent enough, and the Trojans (thinking the horse a trophy) pulled it into their city themselves. The Greeks, under the cover of night, left the horse, opened the city gates, and allowed the rest of the Greek army into the city. The city of Troy was destroyed.
Essentially, the virus works the same. A Trojan Horse looks like something the user will find desirable. Instead, the program creates a virus which can create many issues for the infected computer. The virus can do the following: allow remote access, data theft, modification/copying/deletion of files, and access to a web camera. A Trojan Horse does whatever the creator decides he or she wants done.