The centurion, as Jesus will soon point out, was quite a man of faith! He hadn't come to Jesus personally because he felt unworthy to do so. This man of faith humbled himself before the Lord. In general, it is still true that the more faith one has, the less he will esteem himself. The centurion believed that Jesus could heal his servant regardless of where Jesus was geographically (cf. John 4:50).
The centurion believed that Jesus, like himself, was a man of authority. As a military leader, he knew how to obey those over him and how to command those under him. In order to accomplish a particular task, all the centurion had to do was give the command to his soldiers or servants, and it would be done. The centurion believed that Jesus had those who would come and go for Him and who would carry His messages and enforce obedience to them. Thus, he believed it was enough for Jesus to merely speak the words and the seriously ill servant would be made well.
According to Matthew 8:10, Jesus "marveled" at the man's faith. Jesus is only recorded as marveling twice in the New Testament--once here and again in Mark 6:6 (but on that occasion He marveled because of unbelief).
Jesus declared that He had not found such strong faith yet, not even among the Jews. I believe Jesus was astonished at the greatness of the centurion's faith primarily because the man was a Gentile! It would be expected, perhaps, for an Israelite, educated under the law and the prophets, and prepared for the Lord by the preaching of John, to have such faith in Jesus. But, this man, with the greatest faith exhibited yet, was not a Jew! It should be noted that the surprise of Jesus here is inconsistent with the theory that He, by a direct operation of the Holy Spirit, produces faith in individuals. If He did such, then He would not have marveled on this occasion.
Jesus, in Matthew 8:11, metaphorically predicts the salvation of Gentiles (i.e., those coming "from east and west"; cf. Jer. 16:19). Certainly, He chose to speak on this theme at that time because of the amazing faith of the centurion. However, the thought of Gentiles sitting down (to feast - cf. Luke 14:15ff) with the great patriarchs like Abraham, Isaac, and Jacob would be offensive to most Israelites. This is the case because the common Jewish conception was that the Messiah would come and defeat the Romans in a great war and set up a physical kingdom in Jerusalem similar to that of David's. The kingdom of God would destroy the Gentiles, not embrace them--according to the mistaken thinking of many Jews of that day.
Jesus continues speaking about salvation in Matthew 8:12. Not only would some of the despised Gentiles find salvation, but many Jews (i.e., "the sons of the kingdom") would be cast off. The Hebrew nation was the long-invited guest to God's special feast. However, many of that number would be excluded from the heavenly realm and be left to grieve in the darkness (cf. 21:43; 25:30).
After commending the centurion's faith and speaking briefly about salvation as it pertained to Gentiles and Jews, our Lord healed the servant from a distance with the power of His words. The one who had been suffering greatly was not just relieved but entirely healed immediately. What an amazing miracle! Truly, Jesus is a man of compassion, authority, and power; He is the Son of God!