The faith of the centurion surpassed anything that Jesus had seen in all Israel. The centurion understood the authority position of Jesus. In verse 9 he states that he himself is also a man under authority and he also has men under his authority. When he tells someone to do something, they do it (Emphasis added). Thus he believed that through the authority of Jesus' words it would be done without Jesus actually coming to his home.
I know (I have the faith knowing) if I get caught breaking the law by those in authority over me, I will be punished. How much more valid are Jesus' words Whom has authority over all? How we like the rest of Israel are weak in our faith. Do we completely rely on the authority of Christ? all authority has been given to Him from the Father. Jesus said ask anything in my name and it will be done. I must trust that what Jesus says is valid for me today. How will I trust Jesus' words today to grow in my faith?