I just actually remembered this, it's been such a long time since I've read the novels. It's origin is explained, but not what it actually means, this excerpt is from novel two, chapter four, near the end of the first "scene":
Kyon: "What on earth is a TFEI?"
Itsuki: "It's just an abbreviation we use amongst ourselves, you don't have to know what it stands for. I feel that Nagato-san is the most outstanding one among all of 'them'. I've been wondering, what else is she responsible for besides being a simple communication interface?"
I may read through the novels again during my winter break to see if it's mentioned anywhere else. Also just to read them again.
----
Now, a little something for Christmas, coloured by Phoenix over at the E-H boards.