The Yin and Yang are a circular symbol that represents the opposition of two separate but equal forces. In its shape, which turns and revolves without either side gaining dominance, it shows how forces in nature always strive to seek balance.
Taoism has elements of the Yin/Yang philosophy as its basis; the individual, by practicing Taoism, seeks to gain balance with the Tao, or the natural state of all that is, was, and will be. It is less a form of acceptance -- "what will be, will be" -- and more a form of strengthening the self so nature cannot overpower, but instead is complimented and used as well as it uses. Since Taoism absorbs works from a wide range of authors, it always seeks to find the balance between different philosophies for the greatest compatibility with the basic Taoist beliefs; thus, the Yin/Yang is the balance between the self -- with all its variables -- and the Tao.
Confucianism is more complicated. Briefly, it holds that human beings are capable of improving themselves so that their lifestyles are in sync both with nature and with the humanistic principles of ren (altruism), yi (righteousness), and li (moral behavior). Confucianism is not a theistic belief system, placing all moral decisions and responsibilities on the human being, so all ethical morality stems from action and reaction. In this case, the Yin/Yang is less inherent in the system itself, and instead would be applied to a person's actions in the world; it would be morally obligatory to right your own wrongs, and to intervene in injustices, which in itself returns the inherent balance of the world.