But don't get too excited, I don't think a definitive definition is within reach at this moment. Never the less it's worth thinking about.
The term dantian literally translated means cinnabar field. I don't know the earliest usage of this term but what it refers to is a flat, square, platform of packed earth perhaps as large as one mile square. Raised platforms of this sort were used for state rituals from before written history. One could argue that Beijing has several large "public" squares which are indeed used for state ritual.
Going back into pre-Han (200 BCE) history, it is problematic to used terms like Daoist ritual, Chinese, or even the state. Historians sometimes use words like fangshi or ritual expert to designate the priests or leaders of these rituals if they were not performed by the heads of state themselves.
By Han times, the two most important rituals were the sacrifice to heaven and the sacrifice to earth. Grand rituals which demonstrated military prowess, scale, and unity were also very important. If we look over the scope of time, I think it is sensible to think about a continuum of overlapping ritual traditions. Shamanic journeys on behalf of a ruler, ancestral sacrifice, funerals, rituals for the unresolved dead, theatrical tales of gods and demons, trance possession exorcisms, and Daoist rituals for the rectification of qi--all require a sanctified, ritually purified, space in which spacial and cosmic boundaries are defined. They all require a stage.
The dantian is a stage for the performance of ritual.
This early part of Chinese history also supplies us with two other sources of our tradition.
External alchemy, which should really be called early chemistry, was centered around rituals using a furnace and a cauldron which could be vacuum sealed. Clearly, the dan (cinnabar) in dantain, comes from this tradition in which the most basic experiment separated cinnabar into mercury, lead and other trace elements. The literature of this experimental tradition was highly developed by 300 CE when the Upper Scripture of Purple Texts Inscribed by Spirits, was written (See Early Daoist Scriptures).
Meditation, as we call it today, is first clearly described in the Neiye, which is part of the Guanzi, and dates to approximately 400 BCE. Originally it was a practice taught or practiced by kings. While it is impossible to get inside the minds of those early kings, it is worth noting that this earliest meditation text supplies information about the three walled "quite room" in which this practice was to take place. Diet, posture, incense, and the idea that this meditation would have an effect on the conduct of the kingdom, were all present from the beginning.
Many scholars believe that the Daodejing (~300BCE) was originally written for kings and royal families, but by the time Zhang Daoling became the first Orthodox priest of religious Daoism (1st Century CE) the Daodejing was being taught, along with meditation, to anyone who wanted to learn.
These three traditions ritual, meditation and alchemy merged. By the Tang Dynasty (~600CE), members of the imperial family were studying Dzogchen, Tantric Buddhism, and a new school of Daoism called Shangjing (Highest Clarity). The innovation of the Shangjing school was that it used the metaphor of external alchemy in combination with meditation to create a stage for Daoist ritual to be performed inside the body.
The process of a chemical transformation conceived in alchemy became a way to describe the transformations that take place in meditation. The vocabulary was synchronized so that a discussion of one sounded like a discussion of the other. From that base, and under the influence of Dzogchen and Tantric Buddhism, the complexity and detail of Daoist ritual became internalized. As time passed, Orthodox Daoism (Zhengyidao) adopted the idea that efficacious ritual must take place both outside and inside simultainiously.
To understand the meaning of Dantian, it helps to remember that we are talking about a world in which most people are practicing an animist religious tradition. A tradition in which the world is constantly animated by unseen forces--spirits, ghosts, gods, demons.
The Dantian is a purified stage on which internal ritual takes place, inside an internal world animated by ten thousand unseen forces. The external ritual--the dance if you will--happens both on the stage and in an unseen animated world which is rooted in the dantian.
So the dantian is the place where the inner world merges with the outer world. A still place prepared for ritual. A ritual in which the chaos of the cosmos is danced into the dantian. A ritual in which the chaos of our total inner/out experience is brought into or onto a completely stable, mile square, platform of packed earth.
In Taijiquan, when we say, "Sink the qi to the dantian," this is what we mean.
In internal martial arts we rarely hear about these roots, but clearly the vocabulary is meant to invoke them. It is meant to invoke an animated world in which outer and inner are simultaneously and mutually self-recreating and self-rectifying. A world where the influence and potency of our conduct is with out limits.
All those explanation you have read about the dantian being a point or a ball below or behind the navel, the center of gravity, or a feeling of coordination...they were all correct. It is all those things... and it is also a container big enough to hold the entire ocean, and then some.
From the Daodejing:
I have three unchanging treasures. Hold and preserve them;
The first is compassion, the second is conservation, and the third is not imagining oneself to be at the center of the world.