The royal official said, “Sir, come down before my child dies.” “Go,” Jesus replied, “your son will live.” The man took Jesus at his word and departed. While he was still on the way, his servants met him with the news that his boy was living. When he inquired as to the time when his son got better, they said to him, “Yesterday, at one in the afternoon, the fever left him.” Then the father realized that this was the exact time at which Jesus had said to him, “Your son will live.” So he and his whole household believed.
This is very reminiscent of the healing of the Centurion's servant, but differs in that it was the Centurion who suggested that Jesus need not come, only give an order. Here it was Jesus who took the initiative.
It illustrates that it is Jesus' word that is powerful; it does not take his physical presence for his will to be obeyed. He's the master of the Universe, as the hymn says.
This is another example of a whole household believing. Would that we saw more of that. How sad it is that one member of a household should remain unconvinced. How we must pray for our families. Yet even among the 'household' of the disciples, Thomas was unconvinced. He had a special revelation. Should we ask for such for our sons and daughters? The Nobleman came to Jesus for his son.