A Trojan is a program which infects a computer and allows a hacker to gain entry by one form or another.
A Backdoor Trojan is one which allows sets up some kind of server service on the computer for hackers to channel data through

It is also a slang term for a gay person who likes to give another gay person a big one up the bum
Example 1
Straight IT worker: Hey theres some kind of trojan affecting the server. I hope its not a Backdoor Trojan.

Gay IT worker: OOh I wouldnt mind it, as long as its a big one.
Example 2
Gay guy: Oooh you know that guy we met last night, ooh he turned out to be a Backdoor Trojan, yes, he was at the backdoor trying to screw my data out all night long. I can hardly walk
by Edgar Allen Post September 22, 2006
Get the backdoor trojan mug.