Capernaum is one of those words that has always bugged me because of its pronunciation. One would think it would be straightforward, but you can hear it pronounced here. How do you get a "knee" sound of "n-a"? As a kid, I always figured that Capernaum must be roughly in the same location as Capernium, so it was annoying to find out they were the same place. At any rate, Capernaum is a pretty place to hang out and conduct a ministry since it's on the Sea of Galilee.
Jesus starts collecting disciples, the twelve guys who'll hang out with him throughout his ministry. Either Jesus is extremely charismatic or the disciples are tired of their jobs, because they all readily drop their life pursuits to follow him. He meets two of them, Simon Peter and Andrew, fishing and says, follow me. So they do. In the version I'm reading, the New International Version, he says Come, follow me, and I will send you to fish for people. Fish for people just isn't as poetic as the King James version: I will make you fishers of men.
He gathers a couple more disciples, Zebedee and John, who again drop everything and follow him.
Jesus teaches in synagogues, tells everyone that the kingdom of God is at hand and he heals sick people. It's the healing of the sick that makes him famous. Verse 24 lists the type of people he heals: those which were possessed with devils, and those which were lunatick, and those that had the palsy, according to King James, or those suffering severe pain, the demon-possessed, those having seizures, and the paralyzed according to New International.
In the diverse thousands of denominations which are part of Christianity, you end up with a lot of interpretations about demon-possession. Some denominations feel that the times of demon possession are past; others interpret demon possession broadly to cover problems ranging from disbelief to the perils of modern life to the kind of possession that you need an exorcist to cast out. I view these denominations on a scale of fairly rational people to absolute whacked out crazies. But hey, they all get tax-exempt status on church property and even when they don't respect each other's beliefs, we, as atheists, are supposed to respect (or at least tolerate) them all.