When the rabbis of Jesus’s time would teach, they would refer back to what previous teachers had said and taught as a way to establish their credentials and authority on a subject. Think of it as the oral equivalent of citing academic papers. The people of Capernaum were shocked, then, that Jesus didn’t do this. He said things were true because He was the one who said it. Which is entirely appropriate for God to do, but none of the people knew that’s who Jesus was.
But the demon possessing a man at the synagogue knew who Jesus was, and decided to make a big deal about it. At this point in Jesus’s ministry, He wasn’t trying to announce His status as the Messiah. Therefore, Jesus commands the demon to be silent and come out of the man. When the people see this man in his right mind, they are again amazed at Jesus’s authority.
Because of this, Jesus’s fame spreads again through Galilee, and possibly beyond.
Let us see Jesus for who He truly is, and help us to respond correctly: in repentance and faith.