Holiness is purity, sinlessness, and blamelessness. A holy being is irreprovable in every aspect of life. Christians strive to keep our hearts (the mind, the will) in harmony with God and righteousness. This is holiness.
The new mind cannot approve of sin, but must and will be its opponent. Many of our battles are fought with our fallen and weak human nature – its appetites and desires. Nevertheless, as “New Creatures,” we are separate and distinct from the flesh. The weaknesses and imperfections of the flesh are not imputed to the New Creature in Christ Jesus. Our fallen flesh is reckoned as covered, hidden under the merits of our Lord’s redemptive sacrifice. When we sin, we repent, pray for forgiveness through Jesus's blood, and try again. It is a life-long battle.
The Apostle Peter teaches us how to walk in holiness. 2 Peter 1:5-8, 10 (NKJV), “add to your faith virtue, to virtue knowledge, to knowledge self-control, to self-control perseverance, to perseverance godliness, to godliness brotherly kindness, and to brotherly kindness love. For if these things are yours and abound, you will be neither barren nor unfruitful in the knowledge of our Lord Jesus Christ. … for if you do these things you will never stumble (fall).”
We cannot do these things perfectly. But if added to our faith in Christ, and if we grow all these graces to the extent of our ability, we shall not fall. We work out our own salvation with fear and trembling (Philippians 2:12). We know that the righteousness of Christ is applied to those who desire to forsake sin and pursue “the holiness without which no one will see the Lord.” Hebrews 12:14.