As much as the term qi (aka chi) is tossed around by many people in many different contexts, the meaning of the term qi, and its counterpart the li, at least as they were developed by the Neo-Confucian school of philosophy, are quite straightforward and simple. It is so straightforward that I am surprised that no similiar system was put forward in and school of 'Western Philosophy'.
Before I begin, I would like to clear two things. First, the term "qi" has been used in so many contexts and by so many people since the time of the Hundred Schools of Thoughts, that many uses of the term has nothing to do with the technical use of the term developed in the 1200s by the neo-Confucians. And, much like the word "spirit" in English, the term qi is linguistically slippery. It literally means nothing more then "breath", which is what spirit means in English. But as much as we developed terms from this such as "Holy Spirit" and "Distilled Spirits", the root word qi can be used in many contexts.
The second point is that when I use the term metaphysics in the sense of boring, dense Kantian psuedo-mathematical exposition, not in the sense of crystals, unicorns and UFOs, which of course could be confusing, since qi is often used in the context of this modern misusage of the term.
Anyway, on to my proper exposition. The terms li and qi, as used by the neo-Confucian school, simply refer to the fact that everything is made out of li (pattern or principle) and qi (existence, whether in the form of dynamic energy, or dull matter. One example of this, is that if we have an object, say an orange, we can seperate it into the principle (the round shape, the fact that the volume of the orange equals 4/3pir^3, etcetera. And it is also seen as a combination of the qi, the material ingredients, of the orange. Things that we would call the water and sugar molecules, and the like, or perhaps a combination of the five elements.
No matter what amount of scientific sophistication is put into this concept, the underlying concept remains the same. Also, to go beyond the simple explanation given above (which I must admit bares a great resemblance to the 'West's' all time slice and dice philosophical metaphor, that of the forms), there is another great lovely description of what seperates qi from li.
Simply put, if you take all the qi out of an area, the li still remains. In this way, the li can be seen as a "container" that holds qi and gives it a shape, in much the same way that a cup hold water and gives it shape. And much like a cup, no matter how many times you discard the water (qi) from the cup (li), the cup itself will remain the same. Another example would be a game of chess, no matter how many games you play on a chessboard, you can always play more games on the board, and the rules remain the same, no matter how the pieces are moved. Basically put, li is a set of rules that remain no matter what happens to the physical form around it, and that shape all physical forms.
Although one of the most obvious applications of the concept of li is as a mathematical concept. After all, the truth of math are true no matter what the physical form they are put into. The sun and the earth are very physically different, but they still have areas of around 4pir^2. And, personally, I often visualize the li as a cartesian grid.
However, in addition to tautological truths and such omnipresent characteristics of space as the gravitational constant, the neo-Confucians, being Confucians (although heavily influenced intellectually by the Mahayana) also saw li and qi as ways to express the way that individual people responded to the eternal rules of interpersonal behavior set forth by the Cetra. Although we are all individuals, the social atmosphere around us is part of our movement as much as fish are influenced by the water around them.
Which brings us to our last issue, one which I know through my personal investigations, and not through my readings of the old masters. That is, that there is often a temporary or false li around us, but that is really just a temporary arrangement of qi. For example, in my cup example, the cup holds water, but it not effected by it. It is the li. However, as we all know, a cup is not true eternal li, since a cup can be broken and no longer works to shape other qi. In much the same way, many things that we have probably come to think of as patterns of li, such as air resistance and the bernoulli effect, are not actually the eternal li, but only temporary effects of qi. While a chessboard remains unchangeable no matter how the various games on it go, it is always possible to either take a hatchet to the chessboard, or to just say we want new rules. Thus, most of the things that we think of as "li", or systems of rules in which "qi" manifests, are themselves merely different patterns of "qi". People from different groups would argue the same thing about many of the social rules that many people over the years have thought were immutable and eternal.
Now, whether any true eternal laws of li exist, or whether they are all just a temporary congregation of qi, is probably a metaphysical issue that can not be answered. Be that as it may, people do naturally think of many things in terms of temporary physical manifestations and immutable systems of rules. And that is the simple meaning of the li and the qi.