Wayne Grudem defines Omnipresence as such
"Just as God is unlimited or infinite with respect to time, so God is unlimited with respect to space. This characteristic of God's nature is called God's omnipresence (the Latin prefix omni-means 'all'). God's omnipresence may be defined as follows: God does not have size or spatial dimensions and is present at every point of space with his whole being, yet God acts differently in different places."
A good example of where from Scripture Christian Theists gain this thought is Jeremiah 23:23-24 where God says "Do I not fill heaven and earth?" But throughout scripture there are other allusions to this thought (cf: Ps. 139:7-10; Col. 1:17; etc.).
Cf: Grudem, Wayne, (1994) Systematic Theology: An Introduction to Biblical Doctrine. Grand Rapids, MI: Zondervan.