Reading the Bible through its history, you’re left with a question: just what is the Sabbath rest of God? God rested from His works (3), but after rescuing His people from Egypt, they died in the wilderness (5). Yet after the next generation did enter the Promised Land, David still spoke of another day of rest - and this he wrote from his desk in the Promised Land (7).
Thus, “There remains a Sabbath rest for the people of God” (9).
So what is this rest? It is a resting from works (10) - always has been, since Genesis 2:2. But it can only be entered into by faith (3:19). Thus the rest is the gospel: the good news that one may enter into peace with God apart from works, by faith in the One who justifies the ungodly (Romans 4:5). God does all, for those who trust in His re-creative work (see 2 Cor. 4:4-6). By His work and through faith, we come into His rest.
Thus the entirely ironic command: strive! . . . to rest (11). Strive, in the difficulties of today, to continue in faith, not defecting back to your own works. For in defection, apart from faith, work is all there is. You remain in and under Adam’s curse - literally working to death, in all futility (Genesis 3:17-19).
All of which makes the final paragraph of Hebrews 4 such good news.