Indeed, we feel the depth of what a person says because he speaks convincingly - by virtue of his knowledge of the subject matter. And, the deepest impression is felt when one speaks from his own personal experience - not merely from what he had read from books, or searched on the internet, etc. As the saying goes: "you cannot learn to swim from books. You have to get into the water." A person has to experience what it is like to be in the water before he can swim . In other words, to experience first-hand, rather than in theory. So also, the one teaching you how to swim has to have experienced swimming itself.
This is the kind of teaching the people of Capernaum are hearing from Jesus - He experientially knows what He is telling them! He demonstrates that authority by confronting the unclean spirit in the man. The unclean spirit recognises Jesus, and when Jesus exercises His authority and power, the unclean spirit obeys. Jesus' authority is not coercive or loud, but clear, grounded, and effective. Moreover, Jesus makes a deep impression upon the people, because He speaks with authority.
Let's look into our lives. "Unclean spirits" may not be dramatic possessions, but they are real: habits, fears, resentments, or false beliefs, that diminish our freedom. We often try to manage them on our own. Jesus shows another way - He is present to confront them, and restore us to wholeness.
Lord Jesus, make me whole all the time.