Holiness in Scripture is first and fundamentally God's own character: his absolute moral otherness, his separateness from everything corrupt and finite. It is then the covenantal call for his people to reflect that character in the world.
The Hebrew root qadosh, translated 'holy,' means primarily to be set apart, cut off, distinct. When applied to God it does not primarily describe a list of rules but the nature of who he is: utterly other than his creation, morally pure, consuming in his righteousness. The OT develops holiness in two registers: the ontological (God's inherent separateness) and the covenantal (the call for Israel to be holy as God is holy).
The tabernacle and temple architecture enact holiness spatially: gradations of access marking the approach to the Most Holy Place. Isaiah's throne-room vision (chapter 6) is the canonical center of the holiness motif: the seraphim cry 'Holy, holy, holy,' and Isaiah is undone. In the NT, holiness is not abandoned but relocated and intensified. The Holy One of God becomes incarnate (Mark 1:24).
The Spirit given to the church is explicitly called the Holy Spirit. The people of God are called holy in Christ (1 Peter 2:9), not by their performance but by their union with the Holy One. The call remains: be holy, for I am holy (1 Peter 1:16, quoting Leviticus 11:44).