God, and beneath him the angels, both existing wholly in spirit form, sit at the top of the chain. Earthly flesh is fallible and ever-changing: mutable. Spirit, however, is unchanging and permanent. This sense of permanence is crucial to understanding this conception of reality. One does not abandon one's place in the chain; it is not only unthinkable, but generally impossible. The hierarchy is a chain and not a ladder. (One exception might be in the realm of alchemy, where alchemists attempted to transmute base elements, such as lead, into higher elements, either silver, or more often, gold—the highest element.)
In the natural order, earth (rock) is at the bottom of the chain; these elements possess only the attribute of existence. Moving on up the chain, each succeeding link contains the positive attributes of the previous link, and adds (at least) one other. Rocks, as above, possess only existence; the next link up, plants, possess life and existence. Animals add not only motion, but appetite as well.
Man is a special instance in this conception. He is both mortal flesh, as those below him, and also spirit. In this dichotomy, the struggle between flesh and spirit becomes a moral one. The way of the spirit is higher, more noble; it brings one closer to God. The desires of the flesh drag one down. The Christian fall of Lucifer is especially terrible, because that angel is wholly spirit, who yet defies God, the ultimate perfection.
Modern western culture maintains some of these divisions. Just as Milton's Paradise Lost ranked the angels (c.f. Pseudo-Dionysius the Areopagite's ranking of angels), so Christian culture conceives of angels in orders of archangels, seraphim, and cherubim, among others. The lion is still conceived as the king of the beasts, and the oak as the king of the plants.
Amongst animals, subdivisions are equally apparent. At the top of the animals are wild beasts, who were seen as superior as they defied training and domestication. Below them are domestic animals, further sub-divided so that useful animals (such as dogs and horses) are higher than docile creature such as sheep. Birds are also sub-divided, with eagles above pigeons, for example. Fish come below birds, and are sub-divided between actual fish and other sea creatures. Below them come insects, with useful insects such spiders and bees, and attractive creatures such as ladybirds and dragonflies at the top, and unpleasant insects such as flies and beetles at the bottom. At the very bottom of the animal sector are snakes, which are relegated to this position as punishment for the serpent's actions in the Garden of Eden.
Below animals comes the division for plants, which is further sub-divided. Trees are at the top, with useful trees such as oaks at the top, and the traditionally demonic yew tree at the bottom. Food-producing plants such as cereals and vegetables are further sub-divided.
At the very bottom of the chain are minerals. At the top of this section are metals (further sub-divided, with gold at the top), rocks (with granite and marble at the top), soil (sub-divided between nutrient-rich soil and low-quality types), sand, grit, dust, and, at the very bottom of the entire Great Chain, dirt.
The central concept of the chain of being is that everything imaginable fits into it somewhere, giving order and meaning to the universe.