The phrase eternal life comes from a Hebrew phrase, literally “life in the (coming) age.” For the Hebrews “the coming age” was the age in which God would destroy the power of sin and evil in the world and set up his own rule of love and peace. In the earliest notions of this coming age, it was probably not looked upon as something that would never end; it was not “eternal” in our sense of the word. However, there is no doubt that by New Testament times “life in the age” was looked upon by many Jews as an everlasting experience. In the New Testament it definitely has this meaning, even though the main emphasis is always on the quality of life one experiences when God rules his life. That is, in the Gospel of John eternal life is basically qualitative, but it is also conceived of as life that never ends, because it comes from God.
Newman, B. M., & Nida, E. A. (1993). A handbook on the Gospel of John (p. 88). New York: United Bible Societies.