Peter Brandon emphasizes the mission of Jesus as the Son of Man, who came to seek and save the lost, illustrated through the story of Zacchaeus. He explains the separation between humanity and God due to sin, and how Jesus bridged that gap through His sacrifice on the cross. Brandon uses the analogy of miners trapped underground to depict the spiritual darkness and desperation of those who are lost without Christ. He urges listeners to recognize their need for salvation and to accept Jesus as their Savior, highlighting that true salvation comes from faith in Him alone. The sermon concludes with a call to respond to Christ's invitation for salvation, emphasizing the joy in heaven over one sinner who repents.