v1: In spite of the people's disobedience, the promises from God remain, see Rom 3.3. The challenge to the original readers is clear; do not fall short of God's promises.
v2: Without faith there is no salvation. That was true for the people of Israel coming from Egypt, and that is true for each one who hears the message of Christ. The word has no value if there is no faith. The same gospel is relevant to all.
Some versions read, 'the faith of those who obeyed.' This seems to reference to Joshua and Caleb, the two of the twelve spies who did have faith and did obey.
v3-5: God has entered His rest, the works are finished; He invites us to cease from our works (Rom 4.5) and to enter His rest (Matt 11.30). Faith depends on God to save; the unbeliever depends on his own works (Rom 9.30-32; Ezek 33.13). The scripture refers to "my rest," something of God that we enter into.
v6: There remains an open door; some must enter God's rest; many have been disobedient, and rejected the call from God, but "my house (must) be filled" (Luke 14.24). This is not a sign of desperation from an impotent God, but a sign of grace and love towards sinners.
v7: "Today" is every day; the events described preceded the Psalm by centuries; and the Psalm preceded the Hebrew letter by 1000 years; but it is still "today". As in 3.13, this brings an urgency to the call.
v8-10: Joshua took the people into Canaan, and they enjoyed "rest all around" (Josh 21.44). But there was always a deeper rest to be enjoyed; we must enter into God's rest in salvation in Christ. This is the Sabbath rest, God's rest for us.
There is a similar argument in John 6, concerning the bread of life. Through Moses God gave food from Heaven (Ps 78.23-25), yet the true bread of Heaven is Jesus Christ. The Israelites in the wilderness had tasted the shadow, not the real thing.
v11: The need to press on to enter the rest of God, avoiding the path of disobedience, and learning from the mistakes of Israel.
God has given us encouragements to strengthen us, and to give us assurance and hope, see v12-16.
v12-13: The word of God and its power. We must respect the Word of God as such, that it is living and powerful. We cannot escape its searching, so we should be willing to be examined by God through the word. The verses speak of its penetrating power, even between soul and spirit, which is beyond human understanding. Here is a power that is not of man.
v14-15: Christ our High Priest, and His sympathy. This introduces a section (to 7.28) describing the high priest.
Our High Priest has passed through the heavens, and represents us before God. We are to hold fast what we believe, our confession, the faith, the doctrine, 1 Tim 6.12; 2 Tim 1.13.
Our High Priest has endured temptation; He therefore understands us, with our weaknesses; He has experienced the whole range of human experience, emotion, joys, and sorrows.
Our High Priest remained perfect, without sin. He lived in victory, and we can share in that victory.
Jesus our High Priest, passed through the heavens. This is a Type of the high priest passing through the three curtains into the Holy of Holies. Elsewhere, Paul refers to the 'third heaven' (2 Cor 12.2)
v16: We have access to the throne of grace, through Christ our high priest; not a throne of judgment which brings fear, but a throne of grace which brings hope.
We are encouraged to come before Him (Esth 4.11; 5.2); the golden sceptre is always held out; contrast Lev 10.1-3; 16.2. We have boldness not carelessness. And all our needs are met there.