Now this nobleman was from the city of Capernaum, and had a son back home who was about to die. He had heard stories about Jesus and how he had healed many sick people and had done many miracles in the lives of the people of Israel. But he did not yet believe that Jesus was the Messiah and Savior of the world, whom Moses said would come.
Now let's take up the story in John 4:47-53:
47 When he heard that Jesus was come out of Judea into Galilee, he went unto him, and besought him that he would come down, and heal his son: for he was at the point of death.
48 Then said Jesus unto him, Except ye see signs and wonders, ye will not believe.
In other words, Jesus said that unless he constantly proved that he was sent from God by doing something supernatural, Israel would not believe he was the Messiah (which means Christ or the anointed one). They would not believe by what he said, for faith comes by hearing. They would only believe by seeing, as many people are today.
49 The nobleman saith unto him, Sir, come down ere my child die.
The nobleman, ignoring the point that Jesus was making insisted that if he didn't come with him, his son would die.
But Jesus refused to go with the nobleman, instead he challenged him to believe without seeing:
50 Jesus saith unto him, Go thy way; thy son liveth. And the man believed the word that Jesus had spoken unto him, and he went his way. (bolded mine)
This is what Jesus was trying to get this man to do, believe in His words. And this is what he is attempting to get you to do, believe in his written words. When we believe in the words of Jesus, He will do miracles for us too! Now let's find out what happened after the man believed.
51 And as he was now going down, his servants met him, and told him, saying, Thy son liveth.
52 Then enquired he of them the hour when he began to amend. And they said unto him, Yesterday at the seventh hour the fever left him. (1pm)
53 So the father knew that it was at the same hour, in the which Jesus said unto him, Thy son liveth: and himself believed, and his whole house.
Let me explain. As the man was nearing home in Capernaum, his servants met him to give him the good news that his son's condition had turned around! He was not dead, as everyone expected but rather was doing better. The nobleman began to question about what time it was when his son began to feel better. And just as he suspected, it was the same time he was talking to Jesus, and Jesus had said to him "Your son lives!" (Paraphrased)
When he knew it was the same time, about 1pm the previous day that the fever left his son, was the same time Jesus had said "Your son lives", he and his entire family believed that Jesus was indeed the Messiah, and Savior of the world!
In your time of need, take Jesus at his word and you too will discover that He truly is the Son of God and Savior of the world!