A.B. Simpson emphasizes the superiority of Christ as our Great High Priest over Aaron and the Levitical priesthood, highlighting that Christ's priesthood is established on better promises and a better covenant. He explains that Christ belongs to a superior order of priesthood, the order of Melchizedek, and is from the tribe of Judah, which signifies His royal authority. Simpson elaborates on the eternal and unchangeable nature of Christ's priesthood, His perfect character, and the better sanctuary in which He ministers, ultimately underscoring the efficacy of His sacrifice compared to the old covenant. The sermon concludes with the assurance of Christ's ability to save completely and the call for believers to share this salvation with others.