Therefore He came again to Cana of Galilee where He had made the water wine. And there was a royal official whose son was sick at Capernaum. When he heard that Jesus had come out of Judea into Galilee, he went to Him and was imploring Him to come down and heal his son; for he was at the point of death. So Jesus said to him, “Unless you people see signs and wonders, you simply will not believe.” The royal official said to Him, “Sir, come down before my child dies.” Jesus said to him, “Go; your son lives.” The man believed the word that Jesus spoke to him and started off. As he was now going down, his slaves met him, saying that his son was living. So he inquired of them the hour when he began to get better. Then they said to him, “Yesterday at the seventh hour the fever left him.” So the father knew that it was at that hour in which Jesus said to him, “Your son lives”; and he himself believed and his whole household. This is again a second sign that Jesus performed when He had come out of Judea into Galilee. (John 4:46-54)
I've talked about how all healings in the New Testament are connected to some kind of teaching. In the above passage, what is the teaching? Jesus only says two things: “Unless you people see signs and wonders, you simply will not believe” and “Go; your son lives.” Well, the first statement must be the teaching, and it is, so let's learn from it. This healing is not done in the presence of the people following him. Jesus all but says that the people are relying on the visible excitement of the miracle happening before their eyes, and it is obviously upsetting him. Jesus heals the royal official's son from afar, so afar that it takes about 24 hours for the official to get home, or at least to the place where his slaves meet him (there may be another day's journey still). This healing is done from afar, proving that Jesus' power is no trick. The teaching is that Jesus is God, and he does not need to be in direct contact with a person to heal them. The teaching associated with this miracle is so powerful that the royal official and all of his household believed in him.