What does Hebrews 10:21 mean?

The book of Hebrews often refers to the idea of priests. The priests who served under the old covenant were mortal (Hebrews 7:23), imperfect (Hebrews 7:27), and had to offer their sacrifices continually (Hebrews 9:6–7). The animal blood they offered could never really solve the problem of human sin (Hebrews 9:8–10). God's real purpose in using the old covenant was not salvation, but symbolism. Those aspects of the Old Testament law, even its flaws, were meant to point the way towards the "real" solution, which is Jesus Christ (Hebrews 8:5–6). As one who is fully human (Hebrews 2:17–18), Jesus can serve as a priest for mankind. As one who is sinless (Hebrews 4:15), He can offer a perfect sacrifice, accomplishing what animal blood never could.

Earlier passages also referred to the priesthood of Melchizedek (Hebrews 5:9–10), who the Old Testament describes as both high priest and king (Genesis 14:18). This is just one part of how the writer of Hebrews knows that God intended to replace the old covenant. By promising a priest "after the order of Melchizedek," God was emphasizing that His ultimate plan wasn't going to be fulfilled in the old covenant (Hebrews 7:11). Since Jesus brings a superior covenant (Hebrews 7:18; Hebrews 8:6), Christians have every reason to be confident and courageous in living out their faith (Hebrews 10:19–23.