The strong man in the parable represents Satan, who, fully armed, guards his palace so his goods remain in peace. A stronger one, Christ, overcomes him, seizes his armor, and divides the spoils, which are those freed from demonic dominion and transferred into the kingdom of God. In Luke 11, the strong man is also identified with Christ, who keeps those given to Him, and with the believer, who must guard his mind, lest an unclean spirit return with seven worse. In Matthew 12, Jesus uses the illustration to refute the Pharisees, showing that casting out demons proves Satan has already been bound, defeated in the wilderness temptation. This demonstrates Christ's superior authority and the arrival of God's kingdom. Also see sermons and articles about 'Strong Man, The'.
Luke 11:19-22 And if I cast out demons by Beelzebub, by whom do your sons cast them out? Therefore they will be your judges. But if I cast out demons with the finger of God, surely the kingdom of God has come upon you. When a strong man, fully armed, guards his own palace, his goods are in peace. But when a stronger than he comes upon him and overcomes him, he takes from him all his armor in which he trusted, and divides his spoils.
Luke 11:14-15 And He was casting out a demon, and it was mute. So it was, when the demon had gone out, that the mute spoke; and the multitudes marveled. But some of them said, “He casts out demons by Beelzebub, the ruler of the demons.”