Sitting in Michael's Lap
This is my humble opinion, so please bear with me ...
When I use the word "deep" to describe a piece of writing, I am most often referring to the depths within him/herself that the writer had to delve to write the piece.
Some writing is shallow, and is apparent as such; which is not to say that it is any less worthy for not being woven from the stuff of someone's innermost soul. On the other hand, some writing is very obviously introspective (in the case of the author writing about himself) and/or layered with myriad meanings, which may or may not be obvious to the casual observer. However, it is not simply the existence of these "hidden" meanings, but the lesson that they teach or the statement that they make, that lends "depth" to the writing.
End of babble ...
"Nunc lento sonitu dicunt, morierus"
(Now as I hear this bell tolling softly for another, it says to me, "Thou must die.")