From what I can tell, it's the attribute of God mentioned most often in scripture and the only one triply emphasised.
This triple emphasis comes twice--as quoted above from Isaiah 6:3, and once again in Revelation 4:8.
Holy, holy, holy is the Lord of hosts;
the whole earth is full of his glory!
That God is holy tells us, first of all, that he is the "one and only." He is completely separate from everything else that is. He is transcendent (or other), and distinct from all else in a way that makes him superior to all the rest. There is nothing that rivals him, for he is in a class by himself far above everything else that exists.
God is alone in his holiness. His holiness is closely associated with his glory and his majesty, and his holiness means that he must be held in singular esteem. God's holiness is the grounds for the commands to have no other gods before him, to worship and serve only him, and to treat his name with unique reverence. His holiness is equivalent, in a way, to his deity, his godness. It is what makes him the God, the one whose "name alone is excellent."
Who is like you, O Lord, among the gods?
Who is like you, majestic in holiness,
awesome in glorious deeds, doing wonders?
(Exodus 15:11 ESV)
There is none holy like the Lord;
there is none besides you;
there is no rock like our God.
(1 Samuel 2:2 ESV)
Also included within God's holiness is his moral perfection. God is set apart from all else in his purity; in fact, he is the measure of purity. Out of his holiness comes his necessary abhorrence of all moral imperfection. Habakuk tells us that God's purity makes him unable to look on wickedness with approval, and Psalm 24 tells us that only those who are similarly pure may stand in the presence of our holy God.
Isaiah, then, had exactly the right response when he was brought face to face with the holiness of the Lord.
And I said: "Woe is me! For I am lost; for I am a man of unclean lips, and I dwell in the midst of a people of unclean lips; for my eyes have seen the King, the Lord of hosts!" (Isaiah 6:5 ESV).Here is a man who grasped the "deep trouble" factor of God's holiness! Not one of us can remain standing in the presence of our holy God, because we all fall far short of his glory. Our God is a consuming fire—consuming sin and sinners—because he is holy.
It's a scary thing, isn't it? And the proper response to God's holiness is real fear. This sort of fear isn't a bad thing, for it's fruits are good. Real fear of our holy God is the beginning of true wisdom. It is a fountain of life turning us away from the snares of death (Proverbs 14:27). It is because we fear God's holy response to our unholiness that we throw ourselves on his mercy. It is because we fear God that we understand the true value of what Christ has done for us by saving us from God's holy judgment against our sin.
Our knowledge of God's holiness is a driving force in our sanctification. Reverance for God motivates us to turn away from evil (Proverbs 16:6). It is out of our reverence for a holy God that we submit to him in obedience and conduct ourselves circumspectly before him. Those of us who are his are called to be holy as he is holy. We are called be holy in our behavior so we can be like the One who called us (1 Peter 1:15-17).
Of course, since God alone is holy, the holiness that we are called to show in our conduct is never our own intrinsic holiness, but holiness derived from the only Holy One. The wholly separate God separates us to himself by making us like him: holy as he is holy.
But you are a chosen race, a royal priesthood, a holy nation, a people for his own possession, that you may proclaim the excellencies of him who called you out of darkness into his marvelous light. (1 Peter 2:9)And why does he make us holy? So that we may proclaim the excellencies of the only Holy One, the one in a class by himself far above all others. So that we may give him the glory due unto his holy name.
"Holy, holy, holy, is the Lord God Almighty,
who was and is and is to come!"
(Rev. 4:8 ESV)