There are several discernible character traits in the centurion as described by Matthew and Luke:
First, he cares for and is concerned about his servant. Although the servant is a slave, he does not treat him as one. In fact, he is dear to the centurion, and so his suffering moves the centurion to compassion.
Second, he is humble and sees himself as unworthy as a Gentile to approach the Jew Jesus, whether personally or through the intercession of others. Luke describes this humility more vividly than Matthew does. Christ respects the humble and acts accordingly. The centurion's humility is seen in his consciousness of his own sins and the recognition of Jesus' holiness and excellence.
Third, he has obvious faith in Christ's ability to heal. He knows not to expect a "magical" cure—rubbing an idol or touching a charm. Nor does he ask for a sign that a miracle would be performed. His humility shows his out-going concern for another human being, and it is outstanding because of his rank—people with status are rarely humble. When people are given even a low position or title, they often become inflated with pride, valuing themselves of more importance and worth than is realistic.
The centurion's humility is also unusual due to his ethnicity. Roman soldiers were trained to think of themselves as superior to those whom they conquered and presided over, especially in regard to the Jews, whom they scorned. However, the centurion humbles himself significantly before the Jewish rabbi, Jesus, giving Him great honor by abasing himself to the point that he says he is not worthy even of being in His presence.
The centurion's humility teaches us that the most faithful people frequently consider themselves the most unworthy before God. In contrast, the weakest of people often deem themselves the most worthy. Likewise, a righteous person will readily admit his sinfulness, but the sinner will justify himself.
Jesus calls the centurion's act of faith "great" because he does not ask for any sign but believes in Christ's spiritual, supernatural ability. He does not expect anything visible. Jesus twice refers to a person having "great faith," and in both cases, the person is a Gentile: this Roman centurion and the Canaanite woman who appeals for her daughter's healing (Matthew 15:28). These two miracles show that faith transcends such things as race and birth privileges.
Since the centurion is a Gentile, he has no promise by covenant of God's mercy, as do the Israelites. Thus, for him to have this kind of faith is a rare and great thing. His faith sees Christ's power, and he declares His holiness as a witness to other Gentiles. His faith shows his acceptance and respect of Christ as Savior and his submission to His will. He even believes that no direct contact is necessary for Jesus to perform the miracle! The centurion sees no restrictions on Christ's power and ability to heal his servant. He understands that nothing limits God.
It is interesting that Christ marvels over the magnitude of the centurion's faith. He understands the difficulty with which humans struggle with faith—that we are visually oriented, seeing the physical first and the spiritual second. Indeed, with most, the physical is more real than the spiritual. Yet, the reality is that true power, glory, and love are spiritual. These spiritual things are more real than the physical world that we see and hear. This material world will one day pass away, but the spiritual Kingdom of God will last forever and ever (Luke 21:33; II Peter 3:10; Daniel 7:18).