When Jesus had finished saying all this to the people who were listening, he entered Capernaum. There a centurion's servant, whom his master valued highly, was sick and about to die. The centurion heard of Jesus and sent some elders of the Jews to him, asking him to come and heal his servant. When they came to Jesus, they pleaded earnestly with him, "This man deserves to have you do this, because he loves our nation and has built our synagogue." So Jesus went with them. He was not far from the house when the centurion sent friends to say to him: "Lord, don't trouble yourself, for I do not deserve to have you come under my roof. That is why I did not even consider myself worthy to come to you. But say the word, and my servant will be healed. For I myself am a man under authority, with soldiers under me. I tell this one, 'Go,' and he goes; and that one, 'Come,' and he comes. I say to my servant, 'Do this,' and he does it." When Jesus heard this, he was amazed at him, and turning to the crowd following him, he said, "I tell you, I have not found such great faith even in Israel." Then the men who had been sent returned to the house and found the servant well.
— *Ev 7:1–10
Capernaum is also mentioned by Josephus (Life 72), who was brought there after being wounded in battle:
And I had performed great things that day, if a certain fate had not been my hindrance. For the horse on which I rode, and upon whose back I fought, fell into a quagmire; and threw me on the ground. And I was bruised on my wrist, and carried into a village, named Cepharnome.25 or Capernaum. When my soldiers heard of this, they were afraid I had been worse hurt than I was; and so they did not go on with their pursuit any farther: but returned in very great concern for me. I therefore sent for the physicians: and while I was under their hand, I continued feaverish that day: and, as the physicians directed, I was that night removed to Taricheæ.
Obviously Jesus ben Sapphat couldn't heal directly Josephus because otherwise he would have been killed on the spot by the Romans. The evangelist was trying to explain how Jesus was able to heal his secret friend telepathically, at a (safe) distance.
This gives us the reason of the importance of Capernaum for the Oldest Gospel (*Ev): it was the place where Jesus worked as healer in the legends about Josephus being healed there.