This is a much abused phrase. It is taken to mean “in the now,” “refusing to stray in one's awareness beyond the present.” What the heck is that? How big is the window? Five seconds? Ten years? Zeno's paradox alert.
Think of how mindfulness has been reduced to sport (the Zone) or feats of neurological prowess, however impressive those may be.
But if you take it to mean what Heidegger means (right after the line I just posted on), you see something very interesting.
Again, there is an uncanny parallel to Buddhism. It's called the fourth moment in Dzogchen. There is the present, the past, the future. Then there is the fourth moment. This is the moment at which the nature of mind is happening. Shamatha type mindfulness experience has a “nowness” to it that might function as a gate into this fourth moment.
Now unless you've received mind transmission it's pretty easy to dismiss this as a Platonic illusion of some beyond. But I assure you this fourth moment is possible to experience and is in fact much more intimate than the common sense of “being in the present.” It is much more like “being outside of time.” It's indescribable but real.
Talking of indescribable, Trungpa Rinpoche writes a magnificent piece on it here.
So-called sudden enlightenment needs enough preparation for it to be sudden. Otherwise, it can’t happen at all. If you have a sudden accident in your motor car, you had to have been driving in your car. Otherwise, you can’t have the accident.