This passage of Hebrews encourages Christians to "hold fast" (Hebrews 3:6) despite persecutions and hardships. Most of what we face as believers is not as drastic as it could be (Hebrews 12:4), and God uses those experiences to "train" us into a deeper, stronger faith. Prior verses relied on athletic terminology to depict the way we should approach our own spiritual growth (Hebrews 12:11–12).
A common command given in the New Testament is for Christians to seek peace between themselves and others (Romans 12:18; 2 Corinthians 13:11; 1 Thessalonians 5:13). In fact, this capacity to "get along" is tied closely to our spiritual maturity (James 3:17; 1 Timothy 3:3; Galatians 5:22). This is especially important when it comes to relationships between other Christians. Not only does mutual love serve to build up the church, it is a primary sign to the world that we're disciples of Christ (John 13:35; 1 John 3:14; 4:21).
Along with mutual peace, the writer encourages a life of holiness. Again, this is a common theme of New Testament teaching. Christians are empowered by the Holy Spirit to live godly, righteous, moral lives (2 Timothy 1:7). Sin is always the result of rejecting that power, in some way (1 Corinthians 10:13). Those who persist in sin are proving that they don't have the influence of the Holy Spirit in their lives (1 John 1:6).
