The Deep is sort of a 2nd plateau, the first being basically just an awareness of your mind being (very) noticeably stiller, ie "Hey, my thoughts have stopped--cool." The 1st plateau would occur usually at the 30 minute mark.
The Deep would occur a bit after that, usually at the 45-60 minute mark, occasionally sooner, and it is like the 1st plateau, only much more so--almost like if you were actually scuba diving and you had gone deep enough into the water that you could just barely see the light of the sun above you. The first plateau is characterized by stillness, but The Deep is a profound stillness, stillness to the 2nd power. It struck me, because I realized I had never experienced a stillness like this before in my life.
Body and mind are secondary and not thought of--in fact nothing whatsoever is going through my head, except the awareness of the stillness and calm. Breathing is barely perceptible, heartbeat not felt. It is a significantly refreshing experience.