D.L. Moody emphasizes the profound blessings found in the Beatitudes, particularly focusing on the comfort promised to those who mourn and the meek. He explains that mourning signifies a deep awareness of sin and the need for God's grace, while meekness reflects a humble spirit that trusts in God's plan. Moody encourages believers to embrace these qualities, assuring them that God provides comfort and strength in their struggles. The sermon highlights the paradox of finding strength in weakness and the hope that comes from reliance on God.