Jesus departs for Capernaum, where he teaches during the sabbath.
The people there are quite struck by his teaching, especially because of the "authority" (4:32) with which he speaks.
In the synagogue, a person possessed by a demon disrupts class by shouting, "Let us alone! What have you to do with us, Jesus of Nazareth? Have you come to destroy us?" (4:34).
This demon is pretty smart, being otherworldly and all. He knows that Jesus is "the Holy One of God" (4:34), while the people of Nazareth clearly do not.
But Jesus tells him to pipe down and get out.
The demon chucks the poor guy right into the middle of the synagogue, which is proof of its departure. The narrator underlines that no random guys were harmed in the writing of this story. Jesus is already living up to his promises in 4:18.
Everyone's excited, and they remark that Jesus's words have a lot of "authority" and "power." Just by talking, he is able to give supernatural opponents their marching orders.
Next up, Jesus goes to the house of Simon. Don't worry, you're not forgetting something. Apparently, Jesus has already met Simon, even though we haven't read about it.
Let's take a twenty second time-out to recognize that Luke does not seem to mind starting right in the middle of things or at least after some untold events have happened.
Anyway, Simon's mother-in-law has a bad fever, but Jesus takes care of it—no chicken soup required. The detail that she immediately jumps up and starts to serve them is proof that she really does recover that quickly.
The sun sets and marks the end of the sabbath, which lasts from sundown on Friday to sundown on Saturday. The stipulation is that no labor can be performed on the sabbath (check it out for yourself in Exodus 20:8-11 and Deuteronomy 5:12-15).
People are now free to bring their sick friends and relatives to Jesus for a doctor's visit.
Jesus heals them all by laying his hands upon each one.
Jesus also exorcizes demons. As supernatural beings, they're privy to Jesus's identity as the Son of God and Messiah, but Jesus silences them. What's with all the hush hush?
The next day, Jesus departs Capernaum for a secluded place, while the crowds hunt him down and insist that he stay.
But Jesus sticks to his guns. After all, it's his job to spread the good news of God's kingdom in other cities, too.
Jesus does what he says he will in the synagogues of Judea, which is south of Galilee.