the trojans defeated the greeks by building a large wooden horse and hiding inside it. the greeks thought the horse was a gift from the trojans and took it into their city. at night the trojans came out and killed the greeks, burned their city, and raped their women. not in any particular order.
a trojan is exactly that.
and mike's right, if you ask at a specific security related board, they will swamp you with information
Basically it follows the same ideas as the greek horse, hence the name. It is sent/downloaded onto your computer, usually by an unsuspecting person, often posing as something that it is not, for example it could be called "MicrosoftWord.exe" you open it, and you usually dont see much happen and often the file will seem to dispear, that is just itself hiding from you so to speak. Now that the trojan is running it could be doin all sorts of things such as logging your keys, slowing your computer, and making copies of itself (e.g kazaa trojans spread by making copies of themselves under common kazaa search terms into the kazaa shared folder). To prevent getting a trojan use a virus scanner such as Norton anti-virus. To prevent people from connecting to you if they have got a trojan installed on your computer, use a firewall. Scan your computer regularly for viruses/trojans and only open files if you can trust the source, especially of they are executables.
you can also splice trojans with valid programs. i remember combining a trojan (subseven i think. it was a looong time ago and i was on the wrong side of the fence back then) with random little .exe programs. like that coke joke that would open your cd tray. that was a particular favourite