What does Matthew 8:1 mean?

Over the previous three chapters, Matthew presented Jesus' teaching of what we now call the Sermon on the Mount (Matthew 5:1–2). Jesus had walked up to an elevated spot, likely north of the Sea of Galilee near the town of Capernaum. He sat down, surrounded by His disciples, followers, and a crowd of listeners. His teaching in that sermon astounded the crowds—Jesus not only gave deeper meaning to the Word of God (Matthew 5:17), He corrected the hypocrisy of Israel's religious leaders (Matthew 5:20). And He did so with authority, rather than deferring to the views of other people (Matthew 7:28–29).

Now the sermon is complete, and Jesus comes down from the mountain. The large crowds that have been following Him from town to town grow even larger. They have been impressed by His teaching, as well as drawn from many miles in every direction to see His supernatural healings and casting out of demons.

Matthew 8—9 will describe several instances when Jesus healed the sick and freed the demon-possessed. These records are not necessarily given in chronological order. It was common in ancient writing to collect information by topic, and not necessarily grouping events according to time. Matthew chooses to group Jesus' miracles mostly into one section of his book. The reason for including these events is to show Christ's power over both the "natural" and "supernatural" worlds. These are all evidence that Jesus is truly the Messiah.