Essentially what I understand is that zoe aionios, eternal life, refers to both:
1) to a quality of life. "I came that they may have life and have it abundantly." (John 10:10 ESV) This is the quality of life that is found in the age to come. This is quality of life that is of such a high quality because it involves a deeply intimate relationship with God through Christ. "And this is eternal life, that they know you the only true God, and Jesus Christ whom you have sent." (John 17:3 ESV)
2) to a duration of life. “I am the resurrection and the life. Whoever believes in me, though he die, yet shall he live, and everyone who lives and believes in me shall never die.” (John 11:25-26 ESV) This is the unending duration of the life to be found in the age to come. Because we have eternal life, our life will never end. Our life will never end because the age to come will never end. "Truly, truly, I say to you, whoever hears my word and believes him who sent me has eternal life. He does not come into judgment, but has passed from death to life." (John 5:24 ESV)
Some say eternal life is ONLY a quality of life with no implied duration. Some say it's ONLY a duration. I think that the tendency to restrict the meaning of "eternal life" to only one of these two aspects is overly simplistic. I think it's quite probable that there are shades of meaning here. Different verses emphasize different meanings in this phrase, and some verses emphasize many meanings at once. It isn't a cut and dry, black and white thing.
Also, by way of a rabbit trail, what we have here is a simultaneous now/not yet paradigm.
We have eternal life now, yet we have not yet entered into the full experience of that life. The power and presence of "the age which is to come" has invaded "this present evil age". The kingdom is here, but it isn't fully realized. "The age to come" has commenced and is running along side "this present evil age". When you become a Christian, you are transferred from one age to the other, yet this is only fully realized at the consummation. The kingdom of God is at hand. One day "this present evil age" will be gone and all that will be left is "the age which is to come".
From the NET (New English Translation) Bible Translation notes on John 17:3:
This is eternal life. The author here defines eternal life for the readers, although it is worked into the prayer in such a way that many interpreters do not regard it as another of the author’s parenthetical comments. It is not just unending life in the sense of prolonged duration. Rather it is a quality of life, with its quality derived from a relationship with God. Having eternal life is here defined as being in relationship with the Father, the one true God, and Jesus Christ whom the Father sent. Christ (Χριστός, Christos) is not characteristically attached to Jesus’ name in John’s Gospel; it occurs elsewhere primarily as a title and is used with Jesus’ name only in 1:17. But that is connected to its use here: The statement here in 17:3 enables us to correlate the statement made in 1:18 of the prologue, that Jesus has fully revealed what God is like, with Jesus’ statement in 10:10 that he has come that people might have life, and have it abundantly. These two purposes are really one, according to 17:3, because (abundant) eternal life is defined as knowing (being in relationship with) the Father and the Son. The only way to gain this eternal life, that is, to obtain this knowledge of the Father, is through the Son (cf. 14:6). Although some have pointed to the use of know (γινωσκω, ginosko) here as evidence of Gnostic influence in the Fourth Gospel, there is a crucial difference: For John this knowledge is not intellectual, but relational. It involves being in relationship.