When we say that God is infinite, we mean that he is not restricted by space and time. He exists beyond our universe and beyond the limitations of our three dimensions which are height, width, and depth. He is not constrained by the past, the present, or the future. His capacity is without end. His understanding has no limits. His presence is everywhere. The qualities and attributes he possesses are maximized in their perfection.
Generally, his infinitude is understood in relationship to three primary attributes; omnipresence, omnipotence, and omniscience.
His omnipresence means that he is everywhere, whether it is in or out of the universe, along with any and all dimensions and aspects of existence (Psalm 139:7-12; Jer. 23:23).
His omnipotence means he can do anything that he desires. This is a bit trickier because sometimes people will ask if God can make a rock so big he can’t pick it up. But that is a logical impossibility. God can’t do the impossible, like make round squares. God can only do those things which are consistent with his perfect nature. He cannot, for example, cease to be God (Psalm 90:2). He cannot lie (Titus 1:2). He cannot be tempted by sin (James 1:13). There are things he cannot do because they are against his nature and perfection. So, when we talk about God’s omnipotence we say that God can do anything he desires and has all power to accomplish it (Psalm 115:3; 135:6; Isaiah 46:10).
When we talk about God’s omniscience, we’re saying that God knows all things that have existed, do exist, might have existed, and will exist (1 John 3:20). He has full knowledge of all events everywhere. This means he comprehends the location of every atom in the universe simultaneously - past, present, and future - while also dwelling in the hearts of Christians (John 14:23) and knowing their thoughts (Psalm 139:1,23; Psalm 66:18 ).
So, when we talk about God’s infinite nature, we’re saying that God has no restrictions in space and time, is everywhere all the time, can do whatever he desires, and knows everything about everything.