“As one who had authority, and not as the scribes”
The people were astonished at His teaching, because He taught as one who had authority, and not as the scribes. (Mark 1:22 BSB)
What it sounds like today
He was simply a more confident speaker.
The cultural key
Scribal teaching worked by citation chains ('Rabbi X says in the name of Rabbi Y'), deriving all authority from precedent and tradition. Through the whole sermon Jesus has instead said 'You have heard that it was said… but I say to you,' citing no one, placing his own word beside (and over) received interpretation of Torah. Mark places the astonishment at the very start of the ministry, in the Capernaum synagogue, before quoting a single sermon: the manner alone announced something new.
Recovered meaning
The astonishment isn't about rhetorical polish. A teacher claiming direct, personal authority over the Law's meaning was implicitly claiming an authority his hearers associated with God; the question 'who is this?' hangs over the rest of the Gospel.