Andrew Murray emphasizes the significance of the name 'Jesus,' which means 'He shall save his people from their sins.' He highlights that many Christians overlook the depth of this name and the personal relationship that can be cultivated with Jesus, who is a living Person in heaven. Murray encourages believers to engage in daily fellowship with Christ, as it is through this communion that sin is expelled and holiness is attained. He stresses the importance of removing distractions to focus on Jesus, which leads to a deeper love and service to Him. Ultimately, Murray teaches that true happiness and godliness come from an unbroken relationship with Jesus.