When we have a particularly moving or emotional experience, we often refer to it as "deep". Perhaps this is meant to distinguish it from more "superficial" experiences. I might describe my experience a bit differently. When I'm overwhelmed by something extremely powerful, my perception is that I am deep within something else, something infinitely larger. In effect, what happens is that the more limited, superficial sense of myself that I usually have is subsumed into a reality that is limitless. At the end of the day, the verbal description matters little. The only important thing is the transformation of consciousness into something much, much larger.
Do you have a place where you can cease trying to be anything other than exactly what you are? A place of calm acceptance, a place with no severities. If you are anything like me, there is such a place - but there is a barrier to entry: me or, more specifically, my critical judgement of myself. So I have found that the price of admission to this place of acceptance is the willingness to have that judgement nullified or, at the very least, held in abeyance. If this sounds difficult, know that it is worth the effort. Because, once inside the place to be you, you will also be in a place where you can be anything, or everything - or nothing at all. It is, above all, a place to Be.