Various traditions have their own systems of meditation. But broadly speaking, sitting practice involves not interfering with the contents of consciousness, while still being vividly awake to them. Then something we might call "the sheer fact of consciousness" becomes more salient, first during meditation sessions, then even in the midst of Times Square, and later even in sleep. Normally, we have such a tight association with the particulars of conscious experience that we cannot help but overlook the primary sense of being common to all of them.

I'm sorry if this all sounds like mystical mumbo-jumbo. Language is admittedly a big barrier here.