The theological term for God's all-presence is omnipresence, declaring that God's presence is universal.

Dr Herbert Lockyer comments on omnipresence:

"The prefix "omni" signifies "all". An omnibus is a vehicle for all kinds of persons. This quality indicates that the possessor has power to be present everywhere at the same time. Being human, we can only be in one place at a given time". Dr Herbert Lockyer - All The doctrines of The Bible - Zondervan

It is important to understand that God who eternally is present everywhere has a special place of manifestation. His throne is in the highest heaven (Matthew 6:9 ). No being can rival Him in this ability. There is no escaping God, hiding from God or keeping from Him our most secret thoughts (Psalm 139:2 ). He knows the motives of each persons heart (Matthew 6:3-4 ). He hears the prayers in the secret place and rewards openly (Matthew 6:5-6 ). God in His all-presence witnesses everything.

Hebrews 4:13 "Neither is there any creature that is not manifest in his sight: but all things are naked and opened unto the eyes of him with whom we have to do. "

How we are affected by the truth of His all-presence depends on our personal relationship with Him. The revelation knowledge of God being everywhere present is a delight to those who are in Christ Jesus, who live and walk in the Spirit (Galatians 5:16,25 ). Their joy is to know His presence as Redeemer, Friend, Strengthener, Enabler and Deliverer:

Psalm 23:4 "... For You are with me; Your rod and Your staff, they comfort me."

But, even for the believer, it is with trembling joy that God's all-seeing presence is contemplated. J.I. Packer wrote in his classic book:

"A God whose presence and scrutiny I could evade would be a small and trivial deity. But the true God is great and terrible, just because He is always with me and His eye is always upon me. Living becomes an awesome business when you realise that you spend every moment of your life in the sight and company of an omniscient, omnipresent Creator." J.I. Packer - Knowing God - InterVarsity Press

His all-presence is revealed in Scripture as unchanging, unwelcome, and unfailing.