Chuck Smith emphasizes the significance of the Passover lamb in the context of the final plague in Egypt, where the blood of the lamb served as a protective sign for the Israelites. He explains how the lamb, chosen and slain, symbolized substitutionary atonement, foreshadowing Christ as our ultimate Passover lamb who takes away the sins of the world. The sermon highlights the necessity of applying the blood of Jesus in our lives for salvation and the importance of obedience and faith in experiencing God's grace. Smith draws parallels between the Passover feast and the Christian faith, underscoring the need for remembrance and acknowledgment of God's deliverance through Christ.