Verse sixteen sits at the close of Jesus' conversation with Nicodemus, and the discourse it closes is where the phrase born again enters Christian vocabulary, by way of a translation choice rather than a single settled meaning. Earlier in the same chapter Jesus tells Nicodemus that no one can see the kingdom of God without being born anothen, a Greek word that means both again and from above, and Nicodemus's confused reply, that no one can enter his mother's womb a second time, shows he heard the temporal sense while the discourse plainly intends the spatial one. Raymond Brown's commentary treats the ambiguity as deliberate, a Johannine device used elsewhere in the Gospel, where a character's literal misunderstanding of a double meaning becomes the occasion for Jesus to explain the spiritual sense.
Verse sixteen is usually read as the discourse's summary rather than as part of the wordplay, but it inherits the same logic: eternal life is offered to whoever believes, on the same spiritual register anothen opened a few verses earlier. The born again language that later became a fixed term in evangelical usage traces to this ambiguity, not to any single unambiguous phrase in the passage itself.