What does Matthew 8:8 mean?

Jesus has agreed to a request from a Roman centurion to heal his servant who is paralyzed, suffering, and near death (Matthew 8:5–7). From Luke's report on this same event (Luke 7:1–10), we know that Jesus set out for the centurion's home.

Now the centurion objects to this. He declares that he is unworthy to have Jesus in his house. He calls Jesus "Lord," and it is possible that the centurion recognizes Jesus as the Messiah. He definitely understands Jesus to be a powerful and important person. It may also be that the centurion is being respectful to the Jewish customs, which do not normally allow a Jewish person to enter the home of a Gentile.

Clearly, this military officer understands that Jesus' power to heal is not limited in any way by distance. He says that one word from Jesus will be enough to heal his servant. He will go on to explain that he sees in Jesus the same authority over life and health as he, himself, has over the soldiers at his command (Matthew 8:9). Jesus will remark (Matthew 8:10) that He has not seen this level of faith in His power and authority among any of the Jewish people He has interacted with.