The Witness was the calm voice within, the authoritative voice, the dispassionate voice. It was not controlling, It did not demand or judge.
You found it when you closed your eyes (and emptied your mind, and looked around). It was strong and quiet and ever-watchful. The Witness stood proudly apart from the ego-driven side of the consciousness. It was the Civil Servant of the head... It was consistent and impassive and utterly reliable.
I know what she's talking about. I find you can access it readily when some big physical crisis happens. For instance, when my appendix burst, it was this calm voice inside that said 'Tell your children, phone H, drive to hospital, say such and such' quite emotionlessly. Do you know this voice? I expect everyone has it.
Incidentally Wire-fans, on the principle that in any TV show the characters represent parts of the Self, in The Wire surely Morgan Freeman looky-likey Freamon represents The Witness.