Taoism is the more common spelling in English; however, some people consider the newer and rarer spelling Daoism to be more correct. Please see Daoism for more information on that.
Dao (道 HTML Unicode: & #36947;) written Tao in the older Wade-Giles transliteration), is an Asian philosophy/religion, though it is also said to be neither but rather a way of life. Translated literally it does mean "Way" or "Path". The Dao is the natural order of things. It is a force that flows through every living or sentient object, as well as through the entire universe. Daoism is a tradition that has, with Confucianism, shaped Chinese life for more than 2,000 years. Daoism places emphasis upon individual freedom and spontaneity, non-interventionist government and social primitivism and ideas of self-transformation, and so represents in many ways the antithesis to Confucian concern with individual moral duties, community standards, and governmental responsibilities.
Traditionally, Taoism has been attributed to three sources: the oldest being the mythical 'Yellow Emperor', but the most famous is [Lao zi]?'s (Wade-Giles, [Lao tse]?) 'Dao de jing' (Wade-Giles, 'Tao teh ching'). Lao zi was an older contemporary of Confucius. The third source is [Chuang Tse]?. But the original source of Taoism is said to be the ancient 'I Ching', The Book Of Changes.
The Dao de jing was written in a time of seemingly endless feudal warfare and constant conflict. Lao zi was reflecting on a way for humanity to follow which that would put an end to the conflict. And so he came up with a few pages of short verses, which became the Dao de jing. This is the original book of Dao (Peter Merel's interpolation can be found at: http://www.clas.ufl.edu/users/gthursby/taoism/ttcmerel.htm).
The basic tenets of the philosophy are that:
Much of the essence of Dao is in the art of 'wu wei' (action through inaction). This does not mean, "sit on your ass and wait for everything to fall into your lap." What it really means is a practice of accomplishing things through minimal action -- by studying the nature of life, you can affect it in the easiest and least disruptive way. It is the practice of going against the stream not by struggling against it and thrashing about, but by standing still and letting the stream do all the work.