In his sermon based on Ephesians 6:2-4, Pastor Russ explains five things children owe their parents using the acronym HONOR: Honesty, Openness, None/Non-insistence, Obedience, and Respect. He emphasizes that God has given parents authority over their children, and when children honor their parents as commanded in Scripture, "it may go well with you and you may live long on the earth." This divine promise underscores the importance of children respecting parental guidance and authority.