What does Matthew 8:13 mean?
Jesus has completed His statements about the amazing faith of the Roman centurion and the future inclusion of Gentiles in the kingdom of heaven (Matthew 8:10–12). Now Jesus does as the centurion has asked (Matthew 8:5–9). He heals the man's servant without ever going into his house.Jesus tells the man that it will be done for him as he has believed. Jesus is not telling the centurion that his faith is the power ultimately responsible for the work of healing. He is telling him that what he believed Jesus could do has been done. In other words, Jesus could have healed the servant whether the centurion believed it or not, but his faith in Jesus has proved true. The servant was instantly healed.
For many in that time, this may have been one of the most impressive of Jesus' miracles. To heal a person without being there feels like something only God could do. The fact that Jesus did so provided more evidence that He was the Messiah, the Son of God.