What does Luke 11:21 mean?

Pharisees and scribes from Jerusalem have accused Jesus of working under the power of Satan. Specifically, they have decided that Satan moved Jesus to cast out a demon. Jesus is explaining this doesn't make any sense: why would Satan work against his own cause? And how can they make this claim if they believe their own people are casting out demons through the power of God? If Jesus defeats Satan's work, then the Jewish teachers should know He does so under God's power and God's kingdom has arrived (Luke 11:14–20).

Here, Jesus starts a short parable. The strong man, fully armed, is Satan. He is "god of this world" (2 Corinthians 4:4), the dominant influence over human culture. Up to this point, God has given him significant leeway in leading individuals and nations to do evil. Thanks to his influence over humans and his many demons, his power, authority, and kingdom have been relatively secure.

With the arrival of Jesus, the stronger one, the weaknesses in Satan's kingdom begin to show. Jesus' power during His ministry reveals His authority over demons. His coming resurrection will be Satan's defeat. The Pharisees and scribes need to figure out what side of the battle they're on (Luke 11:22–23). Jesus has proven His authority over demons. His destruction of Satan's entire kingdom is coming.

"Palace" in the Greek can mean castle, fortress, or court. It refers to a living place that is well defended.