Merriam-Webster defines a Trojan horse as "a seemingly useful computer program that contains concealed instructions which when activated perform an illicit or malicious action". When you hear the term "Trojan horse", it brings to mind the story of the Iliad by the Greek poet Homer. In this story, a large hollow wooden horse was filled with many Greek soldiers and brought within the walls of the city of Troy. The soldiers then destroyed the city. The computer version of this is almost exactly the same.
If you have been infected by a Trojan horse it is done by the means of another program, which in this case would be the hollow wooden horse. Inside this program, it is filled with many sub-routines and other functions, which would be like the Greek soldiers. Once this program has been executed, the "soldiers" are now within the walls of your computer, (the Anti-virus and firewall software in this case) and can potentially destroy it as well.
There is a wide range of possibilities for these Trojan horses. I will explain the most popular program, SubSeven. The person trying to get into your (or some other user's) computer will use the program "EditServer" pictured above. Through the use of the "bind server with EXE file" function and the "change server icon" function, this Trojan horse can be disguised as anything the user wants. This is especially dangerous in today's society, with the use of peer-to-peer clients such as "KaZaA", "Morpheus", and "WinMX". With the availability of commercial programs that cost anywhere from $25 to $500+ for free to download, users unknowingly download the Trojan horse programs all the time.