Question: "What does it mean that God is omnipresent?"
The prefix omni- comes from the Latin meaning “all.” So, to say that God is omnipresent is to say that God is present everywhere. In many religions, God is regarded as omnipresent, whereas in both Judaism and Christianity, this view is further subdivided into the transcendence and immanence of God. Although God is not totally immersed in the fabric of creation (pantheism), He is present everywhere at all times.
God's presence is continuous throughout all of creation, though it may not be revealed in the same way at the same time to people everywhere. At times, He may be actively present in a situation, while He may not reveal that He is present in another circumstance in some other area. The Bible reveals that God can be both present to a person in a manifest manner (Psalm 46:1; Isaiah 57:15) and present in every situation in all of creation at any given time (Psalm 33:13-14). Omnipresence is God's characteristic of being present to all ranges of both time and space. Although God is present in all time and space, God is not locally limited to any time or space. God is everywhere and in every now. No molecule or atomic particle is so small that God is not fully present to it, and no galaxy so vast that God does not circumscribe it. But if we were to remove creation, God would still know of it, for He knows all possibilities, whether they are actual or not.
God is naturally present in every aspect of the natural order of things, in every manner, time and place (Isaiah 40:12; Nahum 1:3). God is actively present in a different way in every event in history as provident guide of human affairs (Psalm 48:7; 2 Chronicles 20:37; Daniel 5:5-6). God is in a special way attentively present to those who call upon His name, who intercede for others, who adore God, who petition, and who pray earnestly for forgiveness (Psalm 46:1). Supremely, He is present in the person of His Son, the Lord Jesus Christ (Colossians 2:19), and mystically present in the universal church that covers the earth and against which the gates of hell will not prevail.
Just as the omniscience of God suffers apparent paradoxes due to the limitations of the human mind, so does the omnipresence of God. One of these paradoxes is important: the presence of God in hell, that place unto which the wicked are departed and suffer the unlimited and unceasing fury of God because of their sin. Many argue that hell is a place of separation from God (Matthew 25:41), and if so, then God cannot be said to be in a place that is separated from Him. However, the wicked in hell endure His everlasting anger, for Revelation 14:10 speaks of the torment of the wicked in the presence of the Lamb. That God should be present in a place that the wicked are said to be departed unto does cause some consternation. However, this paradox can be explained by the fact that God can be present—because He fills all things with His presence (Colossians 1:17) and upholds everything by the word of His power (Hebrews 1:3)—yet He is not necessarily everywhere to bless.
Just as God is sometimes separated from His children because of sin (Isaiah 52:9), and He is far from the wicked (Proverbs 15:29) and orders the godless subjects of darkness to depart at the end of time to a place of eternal punishment, God is still there in the midst. He knows what those souls suffer who are now in hell; He knows their anguish, their cries for respite, their tears and grief for the eternal state that they find themselves in. He is there in every way as a perpetual reminder to them of their sin which has created a chasm from every blessing that might be otherwise granted. He is there in every way, but He displays no attribute other than His wrath.
Likewise, He will also be in heaven, manifesting every blessing that we cannot even begin to comprehend here; He will be there displaying His manifold blessing, His manifold love, and His manifold kindness—indeed, everything other than His wrath. The omnipresence of God should serve to remind us that we cannot hide from God when we have sinned (Psalm 139:11-12), yet we can return to God in repentance and faith without even having to move (Isaiah 57:16).