Some days I can't seem to get my head clear; thoughts whirl in a rather futile manner; and in particular I cannot 'wake-up' properly; in the sense that I cannot 'self-remember': cannot get that recognition of Me. Here. Now.
In other words I am not really 'present' in my situation, my life. I am on autopilot, disengaged.
This is one condition that formal meditation training (in various schools) attempts to remedy; by learning either control of thoughts, or Not thinking, or letting thoughts fly through the mind without holding onto any. This is quite difficult, but can work; and then I can bring myself to presentness.
(Some people find that this presentness state is the experience of one-ness; but I tend to regard it psychologically rather than spiritually.)
I don't regard presentness as an especially deep or significant state - nor is is a goal in itself; it is more like a basic pre-requisite for the 'state' of intuition: which I do regard as deep and significant. Intuition is that primary thinking or Final Participation which is the mode of Romantic Christianity. That is what I personally regard as my major life goal.
Nonetheless, presentness is, as I said, a valuable or sometimes essential pre-requisite to higher states; and I have found that it is best attained by a very short sleep - specifically when I experience the momentary absence of deep, dream-less sleep.
This works as a very effective re-boot; both clearing and opening-out my thinking; awakening me, and producing an instantaneous sense of presence: Me! Here! Now!
Of course, not everybody can take a micro-nap at will - nor can we control whether such a period of sleep will drop us into deep sleep rather than into 'REM' dreaming sleep. But I present it as a repeated observation that when it does happen that I have a micro-sleep; it can achieve in an instant what struggling to meditate has failed to do over a period of hours.