A. H. Strong defines omnipresence:

God, in the totality of His essence, without diffusion or expansion, multiplication or division, penetrates and fills the universe in all its parts. (Systematic Theology, p. 279)

Psalm 139:7 says, “Whither shall I go from thy spirit? or whither shall I flee from thy presence?” This is not intended to describe the physical dimension of God as if God pervades the universe like a gas. Rather, God is such that every “where” is immediately present before him. There is no place to hide.

The omnipresence of God thus means he is present everywhere with his whole being at the same time. The great danger to avoid in rightly understanding this attribute is the grievous error of pantheism, which says that God is everywhere, and everything is God. This is totally false. God is everywhere, but everything is not God.