G.W. North emphasizes the transition in the understanding of baptism as articulated by Jesus in Matthew 28:19-20. He explains that the apostles initially baptized in Jesus' name due to their limited revelation and understanding of the full gospel. North highlights that while Jesus did not baptize directly, His disciples acted in His stead, preaching and baptizing under His authority. The sermon points out that Jesus expanded upon John's ministry, focusing on water baptism for the remission of sins while remaining silent on the baptism of the Spirit at that time. This transition marks a significant development in the apostles' mission and the unfolding of the gospel.