The part of the Bible can be divided into two parts.
The first, verses 38-42, speaks of the unwillingness to believe that the Pharisees have. They demand a sign from Jesus for him to prove himself. This is after Jesus had already performed miracles and preached, and right before this demand for a sign he had cast demons out of a man. The Pharisees accused him of casting out demons using demonic power. Jesus refuted them, and instead of conceding that he was right and believing him, they demand a sign. The problem is that the Pharisees do not want to believe. Much has already happened, but they refuse to have faith in Jesus and see that He comes from God. Jesus then gives examples of those who listened without needing signs. Ninevah listened to the prophet Jonah though he performed no miracles, and the Queen of Sheba listened to Solomon even though he performed no miracles. Both Ninevah and the Queen recognized the inherent truth in what was being said, and demanded no more. So Jesus says that he will not give in to their demands and give them a sign, except for the “sign of Jonah”. This refers to his death and resurrection, where just as Jonah was in the belly of a whale, so Jesus will be in a tomb.
The second part refers to what may happen to a person after they have had demons exorcised from them, and then ties into the first part. When a person is cleansed of demons, the demons may yet come back if the person is not on their guard. So with the generation of Jesus’ time, evil will be vanquished, but because they will not accept Jesus and be filled with the Holy Spirit, evil will come back to them.