Hebrews 6:19-20 meaning

In sharp contrast to the warning in Hebrews 2:1, "For this reason we must pay much closer attention to what we have heard, so that we do not drift away from it," this hope we have in Jesus's saving work is an anchor of the soul (v 19). 

For the believer, it is possible to wander from faith, but the hope we have in Christ should be an anchor to our soul, keeping us from drifting from Him. An anchor is a weight; it keeps whatever object it's attached to in place. An anchored ship cannot move. This hope both sure and steadfast (v 19) keeps us firmly abiding in Christ in our daily walk.

The Pauline Author explains the nature of this hope, that it is sure and steadfast, and one which enters within the veil (v 19). This means the hope and anchor is Jesus, our true High Priest. The veil references the Tabernacle's veil that separated the people of Israel from God's presence. Levitical priests were the only ones able to pass through the veil to intercede to God on Israel's behalf. 

Here, in the context of Hebrews, the veil referenced is the true veil in heaven. The veil is where Jesus has entered as a forerunner for us (v 20), on our behalf. This hearkens back to 2:17, "so that He might become a merciful and faithful high priest in things pertaining to God, to make propitiation for the sins of the people."

The Pauline Author is emphasizing (and will continuously do so throughout Hebrews) that Jesus is a better priest and a better hope than the rituals of the Old Testament law. He wants his audience to put their faith in Christ, not to save them from hell (they are already believers), but to endure the sufferings they are experiencing, to push on to maturity, to become inheritors and sons.

Jesus has become a high priest forever, writes the Pauline Author, according to the order of Melchizedek (v 20). The Pauline Author will explain this comparison of Christ to Melchizedek in greater detail in Chapter 7. The essence of this comparison is that Melchizedek was a king and a priest. He predated the birth of Jacob, renamed Israel, as well as Levi. He had no relation to Levi (the tribe from which priests were exclusively chosen), but was called by God to be a priest. 

Melchizedek is only briefly mentioned in Genesis, present in only three verses. The Pauline Author uses this man as an archetype, an example that reveals the type of priest Christ is: a high priest of God, eternal, as well as a righteous king and a king of peace, who blesses obedient followers of God. Christ serves this same role for believers, both priest and king, and we only need Him to approach the throne of God.

We should not rely on earthly priests, or religious ceremonies such as sacrifice. Our hope should not be in men or religious practice. Our hope and anchor should be our High Priest, Jesus. We need to endure, with our eyes set on Christ. He is where our hope lies. He is a forerunner, sitting at the right hand of God now (Hebrews 2:9). He invites us to join Him in reigning, if we are faithful and obedient to God, enduring suffering as He did. As it says in Romans 8:17, "and if children, heirs also, heirs of God and fellow heirs with Christ, if indeed we suffer with Him so that we may also be glorified with Him."