Charles Finney emphasizes the necessity of shedding weights and besetting sins to successfully run the Christian race, drawing parallels to the rigorous training of athletes in ancient games. He explains that the race symbolizes the Christian life, where the ultimate prize is eternal glory with God. Finney outlines the conditions for winning this race, including laying aside unnecessary burdens, avoiding distractions, and maintaining a focus on God's calling. He warns against the dangers of selfishness and the importance of perseverance, urging believers to fully commit to their spiritual journey. The sermon serves as a call to action for Christians to evaluate their lives and remove anything that hinders their relationship with God.