"When Jesus heard this, he was amazed and said to those following him, 'Truly I tell you, I have not found anyone in Israel with such great faith. I say to you that many will come from the east and the west, and will take their places at the feast with Abraham, Isaac and Jacob in the kingdom of heaven. But the subjects of the kingdom will be thrown outside, into the darkness, where there will be weeping and gnashing of teeth.'" NIV translation
This is the first time out of the two in the Bible where we see that Jesus was amazed. Here, we see that Jesus was amazed at the faith that was demonstrated by this Gentile (or former Gentile). The centurion had never met Jesus but had only heard of His authority and believed. Jesus told those following Him that this is the type of faith that saves and that it is the same as that demonstrated by the fathers of the Jewish faith (Abraham, Isaac, and Jacob).
Jesus went on to say that many Gentiles would come to this saving faith while many of the Jews would reject Him.
Those that accept Him will take part in the feast (eternal life) while those that do not will face eternal judgment in Hell.
This reminds us that salvation is not based on who your parents were or even if you believe that a messiah is coming. Salvation is only available through this saving faith in Jesus Christ.
There are those that believe and teach others that a Jewish heritage is like a golden ticket to heaven. There is also a concerted effort to get Jews back to Israel and perceived safety without telling them that Jesus is their only hope for that safety and security for eternity. That is a lie from Satan that is spread by false prophets to deceive the Jewish people and is, in effect, a denial of the complete authority of Jesus Christ.
"Then Jesus said to the centurion, 'Go! Let it be done just as you believed it would.' And his servant was healed at that moment." NIV translation
We do not know whether Jesus continued and was met by the centurion or whether these words were relayed to the centurion by his messengers. In either case, Jesus saved the servant's life (Luke 7:2 tells us that his condition was life threatening) without going into the Gentile (or ex-Gentile's) house. This miracle demonstrated that Jesus had the complete authority to bring life or to impose death.