The term Yin-Yang, sometimes stated Yin and Yang, and the generally recognized symbol originates from China. The more popularly recognized philosophy is from Taoist metaphysics, though it is also found in classical Chinese science, philosophies, medicine, and even martial arts like Taijiquan (Tai Chi Quan), the combative form of Taiji (Tai Chi).
The philosophy is one of balance. For everything there is a counterweight. Shadows cannot exist without light. You cannot recognize the taste of sweet without also knowing sour, or the feel of wet without also knowing dry. Yang is considered the energetic portion, and is represented by the white or light parts of the symbol. Yin is the negative, represented by the black or dark parts of the symbol. Yang is the sunny side of the mountain. Yin is the shaded side. Within any state there must be some of the opposing state. Within Yang there is a spot of Yin, shadows within the light. Within Yin there is a spot of Yang, the light that allows us to see in the shadows.
The symbol itself is called Taijitu, the “diagram of supreme ultimate.” It has had several forms. During the Song Dynasty (960 to 1279 AD) a Chinese philosopher, Zhou Dunyi, (1017 to 1073) discussed and diagramed the Taijitu in the Taijitu shuo. Zhou brought together Chinese Buddhism and Taoism in metaphysical discussions of the Yijing. He used the terms Wuji and Taiji, which may be translated as “Polarity that is Non-Polar.” The more commonly recognized symbol is a Taoist version. While it may seem like art, it is really an artistic representation of math. The article “Yin and Yang” discusses the math that both represent and create the symbol.
It is fair to say that the concept is older than the Song Dynasty, though it is difficult to date a concept. Dates require some from of notation. It is also important to note that the philosophy, and most certainly the Taijitu design, is not wholly unique to China. There are Celtic, Etruscan, and Roman symbols that predate Chinese notations.The Celtic symbol dates to the 4th century BC. Their concept was similar, though it was more of an interweaving of leaves, the entwining of life. Romans used the yin-yang, with the inner dots, as shield designs as early as 430 AD. These other cultures do not specifically identify a yin-yang philosophy, but their creation of similar symbols suggests at least common concepts.
Currently the Celtic, Etruscan, and Roman symbols are referred to as yin-yang, though that name is specific to the Chinese symbol, it having a broader recognition and acceptance. It is not known if there were any cross influences with these cultures. It is more likely that these concepts were independently developed, as they are interpretations of fundamental natural qualities and processes. That said, the Chinese, Taoist philosophy is the more clearly defined and more widely understood.