Holiness, a biblical concept associated with separation from the ordinary or the profane, on the one hand, and connection with God or the divine, on the other. God is supremely or definitively holy and people, things, and actions may be considered holy through association with God. Holiness may also include the ideas of consecration to God and of purity from what is evil or improper.
from ‘Holiness’, in Powell, MA, (ed.), HarperCollins Bible Dictionary
In the temple, Isaiah heard the seraphs sing these words:
Holy, holy, holy is the Lord of hosts;
the whole earth is full of God’s glory.
At the Sacrament of the Lord’s Supper, we say these words in the Sanctus:
Holy, holy, holy Lord,
God of power and might.
Heaven and earth are full of your glory.
Hosanna in the highest.
And especially since it’s Trinity Sunday, we’ve sung Reginald Heber’s words:
Holy, holy, holy! Merciful and mighty
God in three persons, blessed Trinity.
When Isaiah experienced that vision in the Jerusalem Temple, he had no idea that over 2500 years later the Gentiles would be quoting his words in their services of worship. Holy, holy, holy!—but what is ‘holiness’?
Holy, holy, holy. God is holy because God is other than what we are. There is a separation between us and God. It has a lot to do with sin; when we are preoccupied with ourselves, we cannot notice God. But God is holy also because we are finite creatures, while God is infinite. We can’t see God. God is way beyond us.