It may be translated as "rational principle" or "law." It was central to Zhu Xi's integration of Buddhism into Confucianism. Zhu Xi held that li, together with qi (氣: vital, material force), depend on each other to create structures of nature and matter. The sum of li is the Taiji.
This idea resembles the Buddhist notion of li, which also means "principle." Zhu Xi maintained, however, that his notion is found in I Ching (Book of Changes), a classic source of Chinese philosophy. Zhu Xi's school came to be known as the School of Li, which is comparable to rationalism. To an even greater extent than Confucius, Zhu Xi had a naturalistic world-view. His world-view contained two primary ideas: qi and li. Zhu Xi further believed that the conduct of the two of these took places according to Tai Ji.
Holding to Confucius and Mencius' conception of humanity as innately good, Zhu Xi articulated an understanding of li as the basic pattern of the universe, stating that it was understood these principles that one couldn't live with li and live an exemplary life. In this sense, li according to Zhu Xi is often seen as similar to the Dao in Daoism or to telos in Greek philosophy and also to the Dharma in Hinduism . Wang Yangming, a philosopher who opposed Zhu Xi's ideas, held that li was to be found not in the world but within oneself. Wang Yangming was thus more of an idealist with a different epistemic approach.
The philosophical concept of li is inherently difficult to define and is easily mistranslated into various simplifications of the core idea. Many philosophers have tried to better explain it, Alan Watts being one of the prominent 20th century authors on the subject.
The tao is a certain kind of order, and this kind of order is not quite what we call order when we arrange everything geometrically in boxes, or in rows. That is a very crude kind of order, but when you look at a plant it is perfectly obvious that the plant has order. We recognize at once that is not a mess, but it is not symmetrical and it is not geometrical looking. The plant looks like a Chinese drawing, because they appreciated this kind of non-symmetrical order so much that it became an integral aspect of their painting. In the Chinese language this is called li, and the character for li means the markings in jade. It also means the grain in wood and the fiber in muscle. We could say, too, that clouds have li, marble has li, the human body has li. We all recognize it, and the artist copies it whether he is a landscape painter, a portrait painter, an abstract painter, or a non-objective painter. They all are trying to express the essence of li. The interesting thing is, that although we all know what it is, there is no way of defining it. Because tao is the course, we can also call li the watercourse, and the patterns of li are also the patterns of flowing water. We see those patterns of flow memorialized, as it were, as sculpture in the grain in wood, which is the flow of sap, in marble, in bones, in muscles. All these things are patterned according to the basic principles of flow. In the patterns of flowing water you will all kind of motifs from Chinese art, immediately recognizable, including the S-curve in the circle of yang-yin [sic].
So li means then the order of flow, the wonderful dancing pattern of liquid, because Lao-tzu likens tao to water:
The great tao flows everywhere, to the left and to the right, It loves and nourishes all things, but does not lord it over them.
- Chan, Wing-tsit (translated and compiled). A Source Book in Chinese Philosophy. Princeton, NJ: Princeton University Press, 1963.