"Jesus said to him, 'Shall I come and heal him?'" NIV translation
As we see in Luke 7, the elders had plead with Jesus to go with them to the centurion's house and evidently He was on the way when He was met by more messengers from the centurion. Jesus asked them if he still wanted Jesus to come and heal the boy. This may be a little confusing at first but, if we understand that a messenger was spoken to just as if he was the one sending him, it makes sense.
"The centurion replied, 'Lord, I do not deserve to have you come under my roof. But just 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.'" NIV translation
The message that the centurion had sent explained that he understood authority and realized it was not based on physical presence. Real authority can be delegated to others with confidence that something will be done.
The passage uses the word "servant" twice but it has a different meaning in the original Aramaic. As we saw before, the first time "taliyy" is used it describes a young man or boy. The second time "servant" is used, the Aramaic word used was "abdeh" which described a bondslave.
It is believed that this bondslave was a female that had been a slave working off a debt. When she was to be set free, she had chosen to marry the centurion. The Roman soldiers were not allowed to legally marry and have families while they served their traditional ten years but they were married in the sight of God. Even in this, we see that the centurion understood the difference between divine authority and the authority of men.
The centurion had used words from Psalm 107:20 when he had said "just say the word". That Psalm speaks of salvation and the coming of Jesus Christ. Therefore, we know that the centurion at least knew the scriptures and was probably a convert to Judaism through his wife. At any rate, he recognized Jesus as the Messiah and knew of His authority from God the Father.