Those who seek find. The centurion understood what authority meant. He was under authority and knew how to use authority. He came expecting Jesus to use His authority in the supernatural realm just like he used it in the natural realm. His understanding of authority and how it works aided his faith in believing Jesus.
Authority works in the supernatural realm by words.
This is also true in the natural realm. Authority is the power behind the words spoken that gives them the force to accomplish their purpose. Most of the people who Jesus healed in the gospels were healed by the spoken word. The centurion believed the words of Jesus. These words healed His servant.