What does Hebrews 7:26 mean?

According to the author of Hebrews, it makes sense that God's ultimate plan for our salvation would involve a high priest who is eternal, exalted, and without sin. The gist of this passage has been the superiority of Jesus' priesthood to that of the Old Covenant (Hebrews 7:22). Among the points raised so far are that the Old Covenant priesthood was not promised with an oath (Hebrews 7:20), while Jesus was given such a promise by God (Hebrews 7:21). Priests could only serve until death (Hebrews 7:23), while Christ is eternally alive (Hebrews 7:16). Later verses will also mention the fact that human priests have to offer sacrifices for their own sins (Hebrews 7:27), while Jesus is sinless (Hebrews 4:15), and that animal sacrifices can never equal the single, perfect sacrifice offered by Jesus on the cross (Hebrews 9:11–14).

This verse summarizes the overall point of this passage: that Jesus is the perfect, complete fulfillment of God's promised role of high priest. All attributes listed of Christ here correspond to attributes assigned to Jesus elsewhere in the book of Hebrews, as well as the New Testament. Jesus is "holy," meaning "set apart" (John 6:69). He is "innocent" and "unstained" by sin (2 Corinthians 5:21). He is "separated" from sinners, in the sense that He was tempted without falling into sin (Hebrews 4:15). And, Jesus is "exalted" by God (Philippians 2:9).

A fundamental theme of Hebrews is confidence in Jesus Christ. The reason for arguing that Jesus holds a superior priesthood is to encourage believers not to fade under persecution. Instead of falling away, or returning to the imperfect system of Judaism, we should be willing to "hold fast" to the gospel (Hebrews 3:6).