Origins
The word 'eon' (also spelled 'aeon') entered English in the seventeenth century from Latin 'aeon,' borrowed from Greek 'aiṓn' (αἰών), meaning 'age,' 'lifetime,' 'a long period of time,' or 'eternity.' The PIE root *h₂ey-w- (vital force, life, long life) connects it to the concept of life-force and duration. Sanskrit 'āyu' (life, vital force) is a cognate, visible in the traditional Indian medical system 'Ayurveda' (knowledge of life). The English word 'ever' may also be distantly related through Germanic.
Greek 'aiṓn' had an extraordinary semantic range. In Homer, it could mean a human lifetime or the life-force itself. In Plato, it approached the meaning of 'eternity' — the timeless, unchanging reality of which temporal existence is a moving image. In Hellenistic philosophy and Gnostic theology, 'Aeon' became a technical term for a divine emanation, a spiritual being inhabiting the space between the supreme God and the material world. The Gnostic Aeons — Sophia (Wisdom), Nous (Mind), Logos (Word), and others — were personifications of divine attributes, existing in the 'Pleroma' (Fullness) that constituted the divine realm.
The word 'aeon' in its Gnostic sense is capitalized and refers to these divine beings. In its chronological sense, 'eon' (lowercase, usually without the 'a' in American English) means simply an immensely long period of time. The two senses are connected by the concept of duration extended to its maximum: an aeon is time stretched toward eternity.
Greek Origins
In geology, an 'eon' is the largest formal division of the geological time scale. Earth's history is divided into four eons: the Hadean (4.6-4.0 billion years ago, before the oldest known rocks), the Archean (4.0-2.5 billion years ago), the Proterozoic (2.5 billion-541 million years ago), and the Phanerozoic (541 million years ago to the present). Each eon spans hundreds of millions to billions of years. The Phanerozoic (from Greek 'phanerós,' visible + 'zōḗ,' life) — the eon of visible life — is the only one in which complex multicellular organisms have left abundant fossils.
The hierarchy of geological time — eon, era, period, epoch, age — provides English with a graduated vocabulary for temporal scale. An age is thousands to millions of years. An epoch is millions to tens of millions. A period is tens to hundreds of millions. An era is hundreds of millions. An eon is billions. This precision in naming temporal magnitude is unique to geological vocabulary and gives scientists a way to discuss deep time with the same specificity that ordinary language brings to hours, days, and years.
In everyday English, 'eons' (or 'aeons') is used hyperbolically to mean 'an extremely long time': 'I haven't seen you in eons,' 'it took eons to arrive.' This colloquial usage collapses the word's cosmic scale into conversational emphasis, a form of everyday hyperbole that nonetheless preserves the word's core association with vast, almost inconceivable stretches of time.
Proto-Indo-European Roots
The relationship between Greek 'aiṓn' and Latin 'aevum' (age, lifetime, from the same PIE root) is preserved in English through 'medieval' (medius + aevum — the middle age), 'primeval' (primus + aevum — the first age), 'coeval' (of the same age), and 'longevity' (longus + aevum — long life). The PIE root thus produced two parallel families in English: the 'eon/aeon' family through Greek, and the '-eval/-evity' family through Latin. Both encode the same concept — the duration of life, extended from a single human span to the age of the universe.