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The word aeon //, also spelled eon, originally means "life" or "being", though it then tended to mean "age", "forever" or "for eternity". It is a Latin transliteration from the koine Greek word ὁ αἰών (ho aion), from the archaic αἰϝών (aiwon). In Homer it typically refers to life or lifespan. Its latest meaning is more or less similar to the Sanskrit word kalpa and Hebrew word olam. A cognate Latin word aevum or aeuum (cf. αἰϝών) for "age" is present in words such as longevity and mediaeval.
Although the term aeon may be used in reference to a period of a billion years (especially in geology, cosmology or astronomy), its more common usage is for any long, indefinite, period. Aeon can also refer to the four aeons on the Geologic Time Scale that make up the Earth's history, the Hadean, Archean, Proterozoic, and the current aeon Phanerozoic.
Astronomy & Cosmology 
In astronomy an aeon is defined as a billion years (109).
Eternity or age 
The Bible translation is a treatment of the Hebrew word olam and the Greek word aion. Both these words have similar meaning, and Young's Literal Translation renders them and their derivatives as “age” or “age-during”. Other English versions most often translate them to indicate eternity, being translated as eternal, everlasting, forever, etc. However, there are notable exceptions to this in all major translations, such as : “…I am with you always, to the end of the age” (NRSV), the word “age” being a translation of aion. Rendering aion to indicate eternality in this verse would result in the contradictory phrase “end of eternity”, so the question arises whether it should ever be so. Proponents of Universal Reconciliation point out that this has significant implications for the problem of hell. Contrast in well-known English translations with its rendering in Young's Literal Translation:
And these shall go away to punishment age-during, but the righteous to life age-during. (YLT)
Philosophy and mysticism 
Christianity's idea of "eternal life" comes from the word for life, zoe, and a form of aeon, which could mean life in the next aeon, the Kingdom of God, or Heaven, just as much as immortality, as in .
According to the Christian doctrine of Universal Reconciliation, the Greek New Testament scriptures use the word "eon" to mean a long period (perhaps 1000 years) and the word "eonian" to mean "during a long period"; Thus there was a time before the eons, and the eonian period is finite. After each man's mortal life ends, he is judged worthy of eonian life or eonian punishment. That is, after the period of the eons, all punishment will cease and death is overcome and then God becomes the all in each one ( ). This contrasts with the conventional Christian belief in eternal life and eternal punishment.
Aeon may also be an archaic name for omnipotent beings, such as gods.
In many Gnostic systems, the various emanations of God, who is also known by such names as the One, the Monad, Aion teleos (αἰών τέλεος "The Broadest Aeon"), Bythos ("depth or profundity", Greek βυθός), Proarkhe ("before the beginning", Greek προαρχή), the Arkhe ("the beginning", Greek ἀρχή), "Sophia" (wisdom), Christos (the Anointed One) are called Aeons. In the different systems these emanations are differently named, classified, and described, but the emanation theory itself is common to all forms of Gnosticism.
In the Basilidian Gnosis they are called sonships (υἱότητες huiotetes; sing.: υἱότης huiotes); according to Marcus, they are numbers and sounds; in Valentinianism they form male/female pairs called "syzygies" (Greek συζυγίαι, from σύζυγοι syzygoi).
Similarly, in the Greek Magical Papyri, the term "Aion" is often used to denote the All, or the supreme aspect of God. 
See also 
- Math words page 16
- Martin Harweit (1991). Astrophysical Concepts (2nd ed.). Springer-Verlag. ISBN 3-540-96683-8. p. 4.
- Canon F. W. Farrar “Mercy and Judgment” 1904 pages 378-382 "?".
- Thomas Talbott "Three Pictures of God in Western Theology" 1995 pages 13-15 "?".
- Matthew 25:46 Young's Literal Translation
- Matthew 25:46 New International Version
- Matthew 25:46 New American Standard Bible
- Matthew 25:46 King James Version
- Matthew 25:46 New World Translation
- Strong's link for the word Eternal (Aeon) in the Christian Concept of Eternal Life
-  H. D. Betz, The Greek Magical Papyri in Translation, Including the Demotic Spells