Everlasting Life is the unending quality and quantity of life given to those who believe in Christ. Both senses matter: in length (without end) and in kind (the life of the age to come, irrupting now). Christ defines it in John 17:3: this is life eternal, that they might know thee the only true God, and Jesus Christ, whom thou hast sent. It is therefore relational, not merely durational.
(John 3:16 and elsewhere.) Life that is endless in duration and qualitatively the life of the age to come; relational knowledge of God.
John's Gospel uses the phrase about 17 times. It runs from the Bread of Life discourse (Jn 6) through John 17's high-priestly prayer to 1 John's confidence (1 Jn 5:11-13: he that hath the Son hath life).
Sometimes called eternal life; aionios covers both the temporal sense (everlasting) and the qualitative (of the age to come). Both are real.
John 3:16 — "For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life."
John 17:3 — "And this is life eternal, that they might know thee the only true God, and Jesus Christ, whom thou hast sent."
1 John 5:11 — "And this is the record, that God hath given to us eternal life, and this life is in his Son."
1 John 5:13 — "These things have I written unto you that believe on the name of the Son of God; that ye may know that ye have eternal life."
Modern Christianity often reduces eternal life to longer-than-this; John insists it is the new kind of life that begins now and never ends.
John 17:3 is striking: this is life eternal, that they might know thee. Eternal life is defined as relational knowledge of God. The duration follows from the relation: the One known is eternal; the relation, once begun, does not end.
1 John 5:11-13 secures the saint's assurance. Eternal life is given; it is in the Son; the saint may know he has it. Not hope for it — have it. Already-not-yet again: the ‘not yet’ of glorified body is real, but the ‘already’ of eternal life possessed is too.
Greek zôē aiônios.
Greek zôē — life; especially as opposed to death.
Greek aiônios — eternal, of the age.
"Defined relationally: that they might know Thee."
"Eternal life is given, in the Son; the saint may know he has it."
"Relation, not just duration."