What does Luke 5:18 mean?

This occurs in Capernaum, which is "home" for Jesus at this time (Mark 2:1). He might be at Peter and Andrew's house. A crowd has come to hear Him teach, but a small group of men has a different need. Their friend is paralyzed, and the men know Jesus can heal him. But they can't get in the house because of the crowd.

Jesus' primary purpose at this stage in His ministry is to "preach the good news of the kingdom of God" (Luke 4:43). The "good news," ultimately, is salvation: forgiveness of sins and reconciliation with God through Jesus' sacrifice on the cross followed by His resurrection.

Miracles are attention-getting, but they're secondary to the message. Miracles confirm Jesus' teaching, reveal that He is empowered by God (Luke 5:17), and give a foretaste of the complete healing His followers will experience after death. Jesus is personally motivated to heal in response to others' faith (Mark 6:5–6) and out of His own compassion (Matthew 14:14). It is His teaching, however, that put His works into context.

"Paralyzed" is from a root word meaning "feeble, weakened, disabled, or crippled." It's the same term used regarding Aeneas in Lydda (Acts 9:32–33). The extent of the man's condition is unknown, but he is apparently unable to walk. The King James Version uses "palsy" as a short form of "paralysis," but in this context means the same thing.