Jesus leaves home abruptly to go the other side of the Sea of Galilee. Jesus stills the sea, which may foreshadow the stillness He is about to bring to a Gentile demoniac, given the Old Testament association of the Gentile nations and the sea. The event also evokes Old Testament imagery of God’s power over nature, and particularly to quiet the raging and chaotic sea, leaves the disciples wondering without answer about what this says of Jesus’ identity.
Next Jesus enters the Gerasenes. This is very clearly Gentile territory, and the entire episode is characterized by Gentile vocabulary and imagery: swine, uncleanliness, a "legion," and even the classic Old Testament Gentile name for God, "Most High" (υψίστου, which in the LXX translates עֶליוֹן). Just as Jesus as just stilled the chaos of the sea, so Jesus stills the chaos of the demoniac. This time it is not the disciples who experience awe but the locals of the area. They were afraid and begged him to leave, a negative response but still in a sense more respectful than what Jesus has experienced in His own country. It is not entirely fruitless: the former demoniac remains as a permanent testimony and a "down payment" on future fruit among the Gentiles.
Jesus returns across the sea once more, having conquered a legion, and a crowd again gathers by the sea. A ruler of the synagogue, named Jairus, asks for Jesus to heal his daughter, who is on the verge on death. On the way, they are interrupted when a woman with a bleeding problem touches Jesus to be healed. After that the daughter is dead, but Jesus goes anyway and "secretly" raises her. It is interesting to ask why Jairus is named when so few characters in Mark's healing narratives are. Richard Bauckam's thesis that such instances are a narrative method to indicate eyewitness sourcing certainly seems plausible.
Besides this, it is undoubtedly important that the bleeding woman interrupts the matter with Jairus' daughter. The two accounts bear a number of resemblances, such as the figure of 12 years, and both of the healings are of females. In both cases something thinks Jesus is being unreasonable (the disciples because He wants to know who in a crowd touched Him, the mourners at His claim the girl is but asleep). Both also involve secrecy giving way to public witness, as the bleeding woman tried to remain unseen but confesses publicly, and Jesus charged Jairus' family to tell no one, but they did anyway. The healing in both cases is explicitly noted to be by touch (as opposed to speech or being left unspecified).
There are also contrasts. Jairus has rank and requests help from Jesus in a respectable manner; the bleeding woman is unclean and unknown, and her request for help is surreptitious. The bleeding woman is physically alive but dead to Israel and the Temple, while Jairus' daughter is physically dead but had full access and status. Perhaps most strikingly, the bleeding woman gets the special response that her faith have saved/healed her, while Jairus' daughter herself was dead and no comment was made on Jairus' faith.
We have, then, both sides of Israel, the highest and the lowest, both touched by Jesus' power and compassion. That representatives of each side of this spectrum need Jesus shows this need applies to Israel as a whole. Dying and unclean, her only hope is to have faith in Him and be raised by Him from death.
Finally for this passage, Jesus returns home to a cold welcome. They scoff at Him because they have always known Him, and the prophet goes home to less honor than even He was given by the Gentiles of the Gerasenes who sent Him away. Even Jesus Himself is astonished. Does this mean Israel will indeed fail to have faith in Him and be raised by Him?