belonging to the age to come, and so without end: everlasting, eternal
This word is the adjective formed from the noun for an age or epoch (αἰών), so at its root it means "belonging to an age" or "lasting for an age." That is looser than the English "eternal," which can suggest a timeless state standing outside of time altogether. In the New Testament the age in view is overwhelmingly the coming age of God, the unending order that begins with the resurrection, so the word carries two ideas at once that English struggles to hold together. One is sheer duration: something whose end is simply not in view, and that, when tied to God, has no end at all. The other is quality: not just life that lasts forever, but the life of God's new age, a different kind of life altogether.
This is why "eternal life" in John and Paul is not merely survival without end. It is the life of the age to come, already breaking into the present for those who trust Christ, and only fully arriving later. The duration is real, but the emphasis often falls on the quality and the source: it is God's own life, shared.
The same word points the other direction too. When it describes fire, punishment, or ruin, it names the lasting consequence that belongs to that final age, the settled outcome on the far side of judgment. And it describes God himself and the realities tied to him: his glory, his covenant, his gospel, the redemption Christ secured once for all. In every case the thread is the same: this thing belongs to, and shares the permanence of, the age that does not pass away.