Adapted from Wikipedia
A holon (Greek: holos, "whole" + -on, "a part") is something that is simultaneously a whole and a part. The word was coined by Arthur Koestler in his book The Ghost in the Machine (1967, p. 48). Koestler was compelled by two observations in proposing the notion of the holon. The first observation was influenced by Nobel Prize winner Herbert Simon's parable of the two watchmakers, wherein Simon concludes that complex systems will evolve from simple systems much more rapidly if there are stable intermediate forms present in that evolutionary process than if they are not present. The second observation was made by Koestler himself in his analysis of hierarchies and stable intermediate forms in both living organisms and social organizations. He concluded that, although it is easy to identify sub-wholes or parts, wholes and parts in an absolute sense do not exist anywhere. Koestler proposed the word holon to describe the hybrid nature of sub-wholes and parts within in vivo systems. From this perspective, holons exist simultaneously as self-contained wholes in relation to their sub-ordinate parts, and dependent parts when considered from the inverse direction.
Koestler also points out that holons are autonomous, self-reliant units that possess a degree of independence and handle contingencies without asking higher authorities for instructions. These holons are also simultaneously subject to control from one or more of these higher authorities. The first property ensures that holons are stable forms that are able to withstand disturbances, while the latter property signifies that they are intermediate forms, providing a context for the proper functionality for the larger whole.
Finally, Koestler defines a holarchy as a hierarchy of self-regulating holons that function first as autonomous wholes in supra-ordination to their parts, secondly as dependent parts in sub- ordination to controls on higher levels, and thirdly in coordination with their local environment.
Arthur Koestler text on holon
A holon is a system (or phenomenon) that is a whole in itself as well as a part of a larger system. It can be conceived as systems nested within each other. Every system can be considered a holon, from a subatomic particle to the universe as a whole. On a non-physical level, words, ideas, sounds, emotions—everything that can be identified—is simultaneously part of something, and can be viewed as having parts of its own, similar to sign in regard of semiotics.
Since a holon is embedded in larger wholes, it is influenced by and influences these larger wholes. And since a holon also contains subsystems, or parts, it is similarly influenced by and influences these parts. Information flows bidirectionally between smaller and larger systems as well as rhizomatic contagion. When this bidirectionality of information flow and understanding of role is compromised, for whatever reason, the system begins to break down: wholes no longer recognize their dependence on their subsidiary parts, and parts no longer recognize the organizing authority of the wholes. Cancer may be understood as such a breakdown in the biological realm.
A hierarchy of holons is called a holarchy. The holarchic model can be seen as an attempt to modify and modernise perceptions of natural hierarchy. Ken Wilber comments that the test of holon hierarchy (e.g. holarchy) is that if a type of holon is removed from existence, then all other holons of which it formed a part must necessarily cease to exist too. Thus an atom is of a lower standing in the hierarchy than a molecule, because if you removed all molecules, atoms could still exist, whereas if you removed all atoms, molecules, in a strict sense would cease to exist. Wilber's concept is known as the doctrine of the fundamental and the significant. A hydrogen atom is more fundamental than an ant, but an ant is more significant.
The following diagram is from an essay by Andrew Smith, How History Repeats Itself.
A brief history of the concept of holons, by Mark Edwards
Holarchies - essay by Flemming Funch, 4 Feb 95, with diagrams.
Ecosystems and Holarchies - a new way to look at hierarchies
Koestler, Arthur, 1967. The Ghost in the Machine. London: Hutchinson. 1990 reprint edition, Penguin Group.