Chuck Smith emphasizes the mightiness of God as depicted in Zephaniah 3:17, illustrating His power, wisdom, salvation, joy, and love. He highlights that God is not only mighty in creation and salvation but also rejoices over His people and dwells among them. Smith encourages believers to recognize God's presence and love, assuring them that He is a source of joy and rest. The sermon calls for a personal acknowledgment of God's dwelling in our lives, emphasizing the importance of faith and obedience to His commandments.