F.B. Meyer emphasizes the power of claiming God's promises in prayer, as exemplified by David's plea in 1 Chronicles 17:23-24. He encourages believers to confidently present specific promises from Scripture, asserting that true prayer aligns with God's will and seeks to magnify His name above personal interests. Meyer highlights the beauty and strength found in this approach, urging Christians to focus on God's glory rather than their own desires. By doing so, they can experience a deeper connection with God and witness the fulfillment of His promises.