The Dao 道
The text uses Pinyin, the current intenational standard. The older Wade-Giles which is still used in in parentheses.
The Dao (or Tao) is The Way or more concretely the path. The Daodejing (Tao te Ching), written in around 530 BC, attributed to Laozi (Lao Tzu) is considered the founding text for Daoism as a philosophy. The first verso of the Daodejing (Using Legge's and Muller's translation):
The Dao that can be trodden
is not the enduring and unchanging Dao.
The name that can be named
is not the enduring and unchanging name.
If we perceive it as having no name,
it is the Originator of heaven and earth;
If we give it a name,
it is the Mother of all things.
Always without desire
we see the mystery,
But we desire,
Only the outer fringe we shall see.
These two aspects, really the same;
though we give it different names.
This sameness is the mystery,
A mystery within mystery;
The door to all marvels.
It is mysterious, but still, at least until we examine it. Then it becomes the Mother of all things. As the idea of Yin and Yang developed, it becomes the Mother of all things changing, in a Yin-Yang cycle, each according to its nature.
As the Yin-Yang of nature was observed and the Yin-Yang exhibited as a life-force, this was called Qi (Chi, Ch'i).
This manifests itself in the Yin-Yang symbol, where the light, energetic, creative, force has a small dark dot, the potential within it for change. The dark, passive, receptive force which draws the light to it, to grow, but retains the light dot, the potential for the creative. This is the Law of Change manifests in the I Ching.
The unbroken, light, yang lines combined with the broken, dark, yin lines to make up the 8 Trigrams and 64 Hexagrams. As they interact and change, it becomes a model of the dynamics of the Universe and of human interactions
The Law of Change leads to what Carl Yung calls synchronicity. Things do affect each other, even when there is no apparent cause and effect relationship. So, when you cast the coins or manipulate the yarrow stalks, this idea of the Dao from which all things arise, yin-yang manifests itself, the cycles of nature work in synchronicity, it is said that you are participating in this very cycle as the coins fall and the stalks are laid down in carefully counted piles.