Just as he who called you is holy, so be holy in all you do; for it is written: "Be holy, because I am holy." -1 Peter 1:15-16
Holy is the way God is. To be holy he does not conform to a standard. He is that standard. He is absolutely holy with an infinite, incomprehensible fullness of purity that is incapable of being other than it is. Because he is holy, all his attributes are holy; that is, whatever we think of as belonging to God must be thought of as holy. -A.W. Tozer
When examined at their deepest level, every doctrine comes back to the holiness of God. It is vitally important to grasping justification, sanctification, redemption, grace, etc. Without a robust and thorough understanding of the holiness of God, little of who He is, what He does, and what He requires makes sense. God is separate, set apart, and distinct from everything in His creation. This also involves His perfectly pure moral standard. He is good because He is holy. He is perfectly just because He is holy. All of these things come back to His holiness. When Isaiah is faced with God's holiness and glory in chapter 6, he is forced to measure himself against that perfect standard and realizes that he is filthy. He even thinks he will be ruined because of his imperfection in the presence of a holy God.
Christians often see the redemption and salvation through the death and resurrection of Christ as the most important and essential doctrine of our faith. However, God's redemption and salvation don't make sense apart from the context of God's holiness. There is something that we had to be saved from, namely our own sin. There was a desperate need to be redeemed by the blood of Christ because the result of our sin is the wrath of God.
Something that is common to hear from skeptics is, "How could a good God be also full of wrath? That doesn't sound loving or good to me." Without knowledge of God's holiness, this question is certainly reasonable. However, keeping in mind that God is holy and perfect, how could He NOT punish sin? If God did not abhor sin and did not desire to banish it from His presence, He would not be good. God's wrath is the manifestation of His holiness. He cannot look on sin and accept it. Otherwise, He would not be good and just. Imagine that a judge presided over a case where there was overwhelming evidence to convict the suspect of a murder that had been committed. We would be outraged if the judge let the man go free without punishment. We would not say he was a good and just judge. God's justice and wrath is evidence of His perfect goodness and holiness. He cannot allow sin. He would not be holy if He did.
Now, the truly unfathomable mystery of God's holiness is that it led Him to engineer a plan that would be the greatest injustice in the history of His creation. He came to Earth as a perfect man, retaining all of His holiness, and bore the wrath that was meant for our sin. He was perfectly innocent, deserving none of the penalty. Yet, He took it because He loved us and wanted to take away that sin so that He might make us holy through the blood of Christ. He was tempted in every way, just as we are, yet did not sin. Even so, He was pierced for our transgressions and crushed for our iniquities. Without an appreciation for the holiness of God, the cross doesn't make sense. God's holiness keeps Him from tolerating sin but it also is the source of His unconquerable love which conquered the grave for us, if we accept the blood of Christ to cover our sins.
From a sinful human perspective, God's command to be holy as He is holy is impossible. In our natural, sinful state, we can only exclaim that we are men of unclean lips and deserve ruin. But through the holiness afforded to us by Christ through His perfect, holy sacrifice, we can be holy as He is holy. No wonder the Gospel is called Good News.