Mark does not tell us what Jesus said in that synagogue, but we know that people are astonished at His teaching because Jesus teaches "as one with authority" and not like the scribes.
The Greek word for authority, exousia, is also translated as 'power.' Those two words occur one hundred times in the New Testament. Authority is defined in the Blueletter Bible as "the power to do as one pleases." [The Greek root exesti means "it is lawful"] The word exousia is a composite of the preposition ek, "out of or from," and ousia (from eimi) which is the verb "to be." Authority/power comes from the being of the person, or from who a person is. God use the verb "to be" to answer Moses' question "Who are you?" "I am" says God, "Tell them 'I am' sent you." [The Hebrew hayah is translated ego eimi in the Greek Bible, which is Jesus' preferred usage to refer to Himself in the Fourth Gospel] Quite literally, all power and authority come from God, and in Jesus, God become Human, the authority is palpable.
While palpable, I doubt the people could define what they experienced. They knew He was different from the religious leaders who taught them. They felt the power in His words---a power to reveal God, forgive sins, heal people and free them from demons. Jesus' speech has life giving, life changing power. It is divine speech.
Remember that in Genesis God speaks the heavens and the earth--God said "let there be" and "it was". The question* is, did creation end with the seventh day? In one sense, yes, but in a real sense, God is still in the process of (speaking creation) creating the world which He intended from the beginning. It is not done yet! So redemption may be seen as the process of recapturing what is gone astray, reshaping what is gone wrong, healing what is broken, and making constant improvements and adjustments. So Jesus' words continue God's creative work! The Father's goal is to make all things one in Him (e.g. Colossians 1:15ff) Theosis, that love-union, is the creative power of God's Holy Spirit at work within us. As we see in that synagogue, this power of God casts out the lies and demons which cripple us. It frees us from the sinful passions which rule and ruin us. The Holy Spirit completes our salvation.
Of key importance, though, is Jesus also shares His power with us. The Trinity actually live within us. This union empowers and authorizes us as minister of salvation light to the world. God redeems us for the purpose of uniting us to Himself in love and authorizing us for the salvation of all creation. As the saving love of God is ever flowing into us, so it must constantly flow out of us as healing salvation for others. (Mt 10:8 Jesus said, "What you have received as a gift, you must give as a gift." see Agnes Sanford's "Healing Light")
So, of course, we must see ourselves as parishioners in that synagogue hearing Jesus' word and opening up to His power cleansing our minds and hearts of all that is unclean. We need constant healing of body, soul and spirit. We received His salvation, but that is the beginning, not the end. We are His Body, the church, so we must also see ourselves (in union with Jesus) proclaiming the message and casting out the evil which afflicts the lives of others. That is the faithful work of love and gratitude. That is where we usually drop the ball. We become disciples but fail to be apostles. We do not understand this theosis/union.
We are the Word incarnate until Jesus returns in glory. We have the power and authority to do as we please in His Name--so let us choose to do what pleases Him. We are the Spirit-filled children of God--so let us live as true children of God. So whom will God amaze through you in the week to come?
*perhaps a clue in John 5:16-17 Jesus defends His miracles on the Sabbath saying, "My Father is working until now and so I am working''
I will give thanks to the Lord with my whole heart (Ps 111:1)