What does Matthew 8:16 mean?
Jesus has just healed Peter's mother-in-law from a fever (Matthew 8:14–15). Next, Peter opened his house for the evening to others in need of healing or who were oppressed by demons. Jesus served them all, casting out demons with a single word and healing everyone who asked from whatever sickness they had.Demon possession—or oppression—seems to have been more common during this time in the history of the world. That speaks to Satan's cleverness and strategy. In that culture, the existence of demons was not debated. There was no reason for the Devil to be especially subtle or hidden. So, demonic work of afflicting human beings was on display in many communities for all to see. In many modern cultures, as belief in demons wanes, it seems to have become more advantageous for Satan to be hidden and secretive.
This verse also shows that not all sickness came from demon oppression. Those were two separate categories.
The fact that Jesus was able to cast away demons with a single word was impressive and demonstrated His authority over the supernatural world. Others during this time provided exorcism services, with various degrees of success. Some tried to make use of what were thought to be magical incantations. Some tried to pit demons against other demons in order to get rid of them. Jesus simply ordered them to leave. They recognized His authority, and they left (Matthew 8:8–9).