I'm not sure I see the point of the translation layer as explained here. The rest of it makes very good sense: the core layer allows you to communicate with any database by just extending a class; and the application layer handles all the "thinking" while the display layer formats it to whatever format you want to use.
But that translation layer sounds like mumbo jumbo...
Now I can see it working if we have a separate layer that builds data structures. IOW, the data structure layer orders the data using the core layer to access the db. Perhaps that's what he means, and he wants this data structure layer separated into 4 different files so that you don't end up with one HUGE class that does everything-- retrieving, updating, deleting, etc.
I think I would rather have it all together... but then again I'm self-taught, so maybe that would be a better way.
FWIW, that's the way I see it.
BTW, sounds like PHPLib would work very well for you-- it has auth/sessions/templates all together in one package. Using this, all you would have to do is build objects in the translation(?) layer, and scripts which would access the objects and hand out data to the templatess.