I will refrain from sharing my opinions or insights concerning this quote. Like picking up the chord progression to an unfamiliar song at a jam session, Lao Tzu works best when you stop thinking about the details and trust your intuition.
The quote comes from Chapter 48 of the Tao Te Ching:
In the pursuit of learning, every day something is acquired.
In the pursuit of Tao, every day something is dropped.
Less and less is done
Until non-action is achieved.
When nothing is done, nothing is left undone.
The world is ruled by letting things take their course.
It cannot be ruled by interfering.