F.B. Meyer illustrates the significance of Esther's approach to the king as a powerful metaphor for our relationship with God. He emphasizes that, like Esther, repentant sinners can approach God with confidence, knowing they will not perish at His mercy seat. Meyer encourages those with petitions to bring their requests boldly before God, assuring them that He is gracious and attentive to their cries. He also highlights the selfless dedication of Christian workers who, like Esther, sacrifice for the sake of others, finding favor with God as they align with His redemptive purpose.