Citation: John 4:46-54, Jesus returns to Cana, where he had turned water to wine; John explicitly numbers this "the second sign."
Narrative
A royal official (basilikos, an officer in Herod Antipas's service) whose son is dying at Capernaum hears that Jesus has come from Judea to Galilee. He goes to Cana and begs Jesus to come down and heal his son.
Jesus says, "Unless you see signs and wonders, you will in no way believe." The official presses: "Sir, come down before my child dies." Jesus answers, "Go your way. Your son lives." The man believes the word Jesus spoke and starts home. On the way his servants meet him with news that the boy is recovering. He asks the hour he began to mend: "Yesterday at the seventh hour the fever left him", the very hour Jesus had said, "Your son lives." So the father, and his whole household, believe.
Theological significance
Faith in the bare word. The man comes wanting Jesus to come down and act in person. Jesus heals instead by a word spoken miles away, and the man's faith grows in stages: he believes the word and leaves (before any evidence), then believes fully when it is confirmed, and his whole household with him. John traces a maturing faith, from need, to trust in the word, to settled belief.
The critique of sign-dependent faith. "Unless you see signs and wonders…" is a gentle rebuke of a faith that requires spectacle. The official rises above it: he takes Jesus at his word. John will later bless exactly this, "blessed are those who have not seen and yet have believed" (John 20:29).
The Cana bracket and the "signs" structure. John organizes Jesus' early ministry around numbered signs; this "second sign," like the first ([water into wine]), happens at Cana, bracketing the Galilee-and-Samaria section (John 2-4) and building toward the fuller revelation in the discourses.
A note on identity
This royal-official miracle is sometimes confused with the [centurion's servant] (Matthew 8 / Luke 7). Most interpreters keep them distinct: a Gentile centurion whose servant is paralyzed (Synoptics) versus a royal official (likely a Jew in Herod's court) whose son has a fever (John); different settings, persons, and details. A minority treats them as one event variously told. The question is noted here and the two are kept separate, as the texts present them.