What does Mark 1:39 mean?

This verse is a summary of the next several chapters; it doesn't mean that Jesus and the disciples made a long trip that wasn't recorded. After preaching and healing in Capernaum, Jesus takes His first disciples "throughout all Galilee" to spread the gospel. The Jewish historian Josephus estimated that at least 15,000 people lived in this area, a much larger region than Capernaum, which may have held only a couple of thousand people.

Again, Jesus preaches in the synagogues (Mark 1:21) just as Paul did in his travels throughout Asia Minor (Acts 13:5, 14; 14:1; 17:17). This underscores that Christianity is not an aberrant cult of Judaism, but is the God-ordained culmination of Judaism (Hebrews 7:11–22). Jesus taught from the Old Testament and explained how the Jewish Holy Scriptures point to Him as the Jewish Messiah (Luke 4:16–21). He was not trying to draw people away from Judaism. Rather, He sought to help them realize what Judaism was about all along. He was never shy about teaching in front of religious scholars. In a better world, they would have accepted His teaching and become leaders in the church. But pride of position and pride of knowledge kept their ears closed and turned these men into the enemy of the same Messiah for whom they claimed to look.

Jesus wouldn't force the Jewish scholars to follow Him, but He had no problem getting rid of demonic obstacles. Casting out demons became a major part of Jesus' public ministry. Demons are mentioned sixteen times in Mark in addition to the many references of unclean spirits. Jesus often cast out demons and healed physical ailments in the same gatherings, and in the ancient world physical and spiritual problems were often spoken of together. Though there may be connections, it is important to treat physical and mental concerns with professional help regardless of any potential spiritual connections.