“Now Moses was faithful in all God’s house as a servant, to testify to the things that were to be spoken later, but Christ is faithful over God’s house as a son. And we are his house if indeed we hold fast our confidence and our boasting in our hope.” (Hebrews 3:5-6)
The original audience of Hebrews was composed primarily of Christians who had converted from Judaism. Consequently they held Moses in high esteem. The writer, therefore, had to remind them that Jesus is superior to Moses. As great as Moses was, Jesus is infinitely greater: Jesus gave him the Law and gave him the power and authority to lead the Jews out of bondage.
The reason the writer brings this up is that many in the audience were being tempted to go back to following the Mosaic Law. They thought this might make life easier for them since they were enduring persecution as Christians from both the Romans and the Jews. The problem was that following the Law meant they were rejecting the sacrifice of Christ as the only sufficient means of salvation. They would go back to trusting in the works of the Law for salvation. There was a dangerous attitude to embrace for those who went back to the Law would be guilty of hardening their hearts against God as did the ancient Israelites. They would suffer the same loss of the promise.
Only those who remain in the faith of Christ, who do not fall back into their old ways of living and thinking, those who persevere until the end, these alone show themselves to be true believers. This does not mean that they earn their salvation by their perseverance, suffering, good works or law-keeping. Rather their salvation is demonstrated by their perseverance and deeds of faithfulness and righteousness. As good as we humans think ourselves to be, we are all sinners. Good deeds are produced only by the power of the Lord. He works through the Holy Spirit and the church. This does not mean we are perfect nor that we never fall, but we do press on by the power of Christ in the midst of chaotic times.