What is the context?
This verse completes the contrast in 9:11–14. Earlier rites provided the cleansing required within Israel’s worship; Christ’s unblemished offering reaches the conscience. The words how much more ask us to recognize the greater effect of His sacrifice.
The purpose is stated plainly: people are cleansed from works of death so that they may serve the living God. Forgiveness opens into a changed life, rather than ending with an outward religious ceremony.
The word translated serve can mean religious service or worship. That meaning supports the connection between devotion and service; it does not, by itself, exclude prayer, singing or gathered worship.
How is this passage commonly understood?
Calvin and Wesley understand works of death as sinful works that come from spiritual death or lead to it. They read the cleansing as the beginning of service pleasing to God, rather than permission to continue in sin.
They understand the eternal Spirit as the Holy Spirit at work in Christ’s offering. The USCCB note reads that expression as Christ’s enduring risen life. This is a difference among the named commentators; it should not be presented as a single official reading held by every member of their traditions.
Where does this fit in God's plan?
Romans 12:1–2 describes the response to God’s mercy as offering our bodies as a living sacrifice and being renewed in our thinking. This is a life offered in gratitude, rather than another sacrifice that takes away sin.
Ephesians 2:8–10 gives the same order: grace saves, and the life God makes new is created for good works. Hebrews’ call to serve belongs within that purpose.
What is our position?
Our study What Does Worship Actually Mean? understands this verse as forgiveness leading into a life of service to God. Christ cleanses people so that they can serve Him with a purified heart. That service reaches into daily obedience and care for others, beyond the time spent in a gathering.