A.B. Simpson emphasizes the importance of committing our trials to God, illustrating that by trusting Him wholly, we can exchange our anxious cares for His Almighty care. He explains that God's hand humbles us but also lifts us up in due time, encouraging believers to cast their worries upon Him. Simpson reassures that God is capable of sustaining us through our troubles, as He carries the weight of our burdens and looks after our interests when we trust and obey Him. The sermon calls for a complete surrender to God's will, allowing Him to take care of our concerns.