When Jesus is on his way to Lazarus to raise him from the dead, Martha first meets Him and later Mary. The Lord has a conversation with Martha and in it He says the words that are among His most famous words from the Gospel of John.
John 11
23 Jesus said to her: Your brother will rise again.
24 Martha said to Him: I know that he will rise again, in the resurrection on the last day.
25 Jesus said to her: I am the resurrection and the life: whoever believes in me, even though he die, will live.
26 And everyone who lives and believes in me will not die, (until) into the aeon. Do you believe this?
resurrection
The subject that Jesus speaks about with Martha from verse 23 onwards is resurrection. In this connection the Lord says that He is the resurrection and the life and that whoever believes in Him will live, even if he dies. The one who dies does not live now, but will live, namely in the future.
fall asleep
The Lord also does not say of Lazarus that he is now dead, but still alive and has lifted up his eyes elsewhere. No, the Lord tells His disciples that Lazarus is sleeping and that He is going to him, to wake Him from sleep. The disciples draw the wrong conclusion from this and say that if Lazarus sleeps, he will recover from his illness. But the Lord had spoken about his death, Lazarus had fallen asleep and had to be raised by Him to live again (John 11:11-14).
will live
In verses 25 and 26 it says that whoever believes in Him will live (future tense), because He will be raised. Those who are raised will live in the future aeon and will not die in that age. The Greek aion is incorrectly translated as eternity in most translations, but an aion is an age (Mark 10:30; Luke 18:30).
aion is not eternity
That aion should not be translated as eternity is also evident here, because if you do render it that way (as the Statenvertaling and NBG translation have done), something is stated that is incorrect: whoever believes in Me, will never die.
Believers also die, but they will live in the future aeon(s) and will not die in that aeon. Unbelievers will not experience these ages. The Lord refers here, among other things, to the words of the prophet Daniel.
Daniel 12
2 And many of those who sleep in the dust of the earth will awake, some to the life of the aeon (Hebrew: olam) and some to the shame and abhorrence of the aeon (Hebrew: olam).