Qi is the most difficult concept to define when discussing martial arts or Chinese medicine. The reason for this difficulty is that term is associated with a kind of mysticism that causes many rational people to dismiss discussions of qi entirely.
Before attempting a rational explanation of qi let me state flatly what qi is not. Qi is not magic. Qi is not a new (or ancient) force that scientists have not discovered or measured. Qi is not electromagnetism or some variant of electromagnetism that acts as a magic force on the world around us. At its simplest, qi was a way to define and classify all those invisible forces that made the world around the observer function.
Consider the wind for instance. What makes the wind move? Without a basic understanding of thermal and fluid dynamics an explanation is difficult, and would depend entirely on your experiences and environment. If you lived near the ocean, you might say that the ocean creates the wind with its vast and rolling waves. If you lived in a desert, you might say that the hot sand reflects the suns energy and causes wind. If it is difficult to describe the wind, think of how much more difficult it is to describe the growth of a tree or the various functions of a human body. From this need, to describe both the interactions of the world around us and the world within us came several cosmological viewpoints of which qi is but one component of one view.
The traditional ideogram for qi represents steam rising from rice as it cooks. You can imagine someone seeing steam from boiling water wisp away on air currents and associate that steam as a visible component of air. Because of this association qi is translated as air or breath, or even breath of heaven. If qi is now both the invisible wind and the visible steam, it must have different qualities at different times. So a hot breath or gust of wind might be called steamy qi, while a cold breeze might be called frigid qi. A strong gust of wind or sudden release of breath is associated to destruction and violence, while a gentle breeze, or relaxed manner of breathing is associated to good health and a pleasant day.
Without a framework to contain these associations they would become unwieldily. The first written attempt at a framework was the Huangdi Neijing. In Daoist thought qi has a metaphysical quality, harmonizing the ten thousand things, interconnecting the universe and man. The Confucian school adopted this concept and applied it to yin and yang theory. Neo-Confucian scholar Zhou Dunyi's Explanation of the Diagram of the Supreme Ultimate, is the best example of this adaptation.
Qi is also discussed in Daoist alchemy as a method towards immortality. By retaining your life qi, and gaining control of when and how you use it, you can become immortal. The primary methods of such control are meditation, exercise, and sexual practices to generate and retain qi. Formulas of potions and elixirs are purported to add qi to the body, and thus extend life. As a component of alchemy qi became its own force, and for those that accepted qi as life force outside normal biological or physiological functions, it became something you can manipulate. If you can retain qi, to prolong life, then you must be able to emit qi to heal or harm another. Unfortunately for many of the daoist alchemist the potions were poison that their physical exercises could not overcome.
A more reasonable approach sees qi as something that needs to be put in order, or balanced. With this approach, qi becomes an activity that is transforming the organs of the human body into different states. Associate these states of qi, and human organs to the Five Phases and you have the basis for Chinese medicine. Finally, a qi driven cosmos meant that there must be a way to anticipate where qi will be in the future, and these attempts to predict the state of qi are called divination. Using yarrow stalks or dice, you can tap into the orderly pattern of the Universe--which is defined by the hexagrams of the Yi Jing--and predict the outcomes of events.
As you can see the simple need to describe something as basic as wind has given rise to an infinite variety of explanations and uses. These attempts, however, only separate qi from its most fundamental definition--that of breath--or create qi as a new force rather than a unifying one. What is qi? To our physical practice qi is breath, nothing more. To understanding the metaphysical interactions of the Wu Xing or the transformations of the Bagua trigrams, qi is a transformative force. Relating the organs of the human body to the Five Phases, or the physical characteristics of a martial posture to one of the trigrams of the Bagua, does not make qi into something more than this basic definition--breath transforms.