Definition of the Tao from Wikipedia -
The Tao can be roughly thought of as the flow of the Universe, or as some essence or pattern behind the natural world that keeps the Universe balanced and ordered.[9] It is related to the idea of qi, the essential energy of action and existence. The Tao is a non-dualistic principle – it is the greater whole from which all the individual elements of the Universe derive. Keller considers it similar to the negative theology of Western scholars,[10] but the Tao is rarely an object of direct worship, being treated more like the Hindu concepts of karma or dharma than as a divine object.[11] The Tao is more commonly expressed in the relationship between wu (void or emptiness, in the sense of wuji) and yinyang (the natural dynamic balance between opposites), leading to its central principle of wu wei (non-action, or action without force).
The Tao is usually described in terms of elements of nature, and in particular as similar to water. Like water it is undifferentiated, endlessly self-replenishing, soft and quiet but immensely powerful, and impassively generous.[12] Much of Taoist philosophy centers on the cyclical continuity of the natural world, and its contrast to the linear, goal-oriented actions of human beings.
[Tao] means a road, path, way; and hence, the way in which one does something; method, doctrine, principle. The Way of Heaven, for example, is ruthless; when autumn comes 'no leaf is spared because of its beauty, no flower because of its fragrance'. The Way of Man means, among other things, procreation. Chu Tao is 'the way to be a monarch', i.e. the art of ruling. Each school of philosophy has its tao, its doctrine of the way in which life should be ordered. Finally in a particular school of philosophy whose followers came to be called Taoists, tao meant 'the way the universe works'; and ultimately something very like God, in the more abstract and philosophical sense of that term.
Relating to Tai Chi, the principles of yielding, softness, centeredness, slowness, balance, suppleness and rootedness are all elements of Taoist philosophy that Tai Chi has drawn upon in its understanding of movement, both in relation to health and also in its martial applications.