NOTE FROM JUNDO: PLEASE SEE MY RESPONSE BELOW.
This is not a philosophical thread. I just realized I have been doing Zazen all wrong till this point. I started only 3 months back so it is not such a bad thing.
What I was doing: Just sitting doing nothing. When awareness comes back by itself to the current moment, then just sit silently again doing nothing.
The correct way: Sit and be present to what is happening in the body-mind. Connect to your senses, listen to what is happening, feel the sensations in the body, attend to whatever is happening in the current moment in your body, watch for the thoughts in your mind. Doing this anchors your awareness to the present moment.
Hopefully I described it right and my practice might still evolve as time goes. Please correct it if you see anything wrong. This whole Zen thing is so confusing! But it works.