A.B. Simpson emphasizes the importance of casting our cares upon God, illustrating how Nehemiah chose to ignore distractions and focus on what truly mattered. He points out that many of our burdens are self-imposed, stemming from worries about things that may never happen. By simplifying our lives and trusting in God's plan, we can find peace and rest, much like a bird resting in its nest. The sermon encourages believers to let go of unnecessary concerns and to trust that God is working for their good.