The black and white halves of the Yin-Yang symbol are similar to the two sides of a coin. They are different, and distinct, yet one could not exist without the other. The circle itself - which contains these two halves - is like the metal of the coin. It is what the two sides have in common - what makes them "the same."
Yin and Yang are the two opposite but yet interdependent energies of life. Each is relative to one another, and can't exist without the other. They arise from a common source, the Tao. Our entire physical reality is based on the interplay of these two energies. http://fractalenlightenment.com/24816/culture/yin-yang-a-symbol-of-balance-and-harmony