A code based on an entirely new, made up language. The language is usually known by a single person (the one who made it up). A code of this sort would theoretically take an eternity to crack, thus giving it it's name.
There is no single Eternity Code; anyone could make up their own, though it would take a lot of time because a whole new language would have to be thought out.
Read Artemis Fowl: The Eternity Code by Eoin Colfer, as I don't have my own example.