"What does it mean that God is infinite?"
 Answer:  The infinite nature of God simply means that God exists outside of and is not limited by time or space. Infinite  simply means “without limits.” When we refer to God as "infinite," we  generally refer to Him with terms like omniscience, omnipotence,  omnipresence.
Omniscience  means that God is all-knowing or that He has unlimited knowledge. His  infinite knowledge is what qualifies Him as sovereign ruler and judge  over all things. Not only does God know everything that will happen, but  He also knows all things that could have possibly happened. Nothing  takes God by surprise, and no one can hide sin from Him. There are many  verses in the Bible where God reveals this aspect of His nature. One  such verse is 1 John 3:20: “...God is greater than our heart, and knows all things.”
Omnipotence  means that God is all-powerful or that He has unlimited power. Having  all power is significant because it establishes God’s ability to carry  out His sovereign will. Because God is omnipotent and has infinite  power, nothing can stop His decreed will from happening, and nothing can  thwart or stop His divine purposes from being fulfilled. There are many  verses in the Bible where God reveals this aspect of His nature. One  such verse is Psalm 115:3:  “But our God is in the heavens; He does whatever He pleases.” Or when  answering His disciples' question “Then who can be saved?” (Matthew 19:25), Jesus says, “With men this is impossible, but with God all things are possible” (Matthew 19:26).
Omnipresence  means that God is always present. There is no place that you could go  to escape God’s presence. God is not limited by time or space. He is  present at every point of time and space. God’s infinite presence is  significant because it establishes that God is eternal. God has always  existed and will always exist. Before time began, God was. Before the  world or even matter itself was created, God was. He has no beginning or  end, and there was never a time He did not exist, nor will there be a  time when He ceases to exist. Again, many verses in the Bible reveal  this aspect of God’s nature to us, and one of them is Psalm 139:7-10:  “Where can I go from Thy Spirit? Or where can I flee from Thy presence?  If I ascend to heaven, Thou art there; If I make my bed in Sheol,  behold, Thou art there. If I take the wings of the dawn, If I dwell in  the remotest part of the sea, Even there Thy hand will lead me, And Thy  right hand will lay hold of me.”
Because God is infinite, He is also said to be transcendent, which  simply means that God is exceedingly far above creation and is both  greater than creation and independent of it. What this means is that God  is so infinitely above and beyond us and our ability to fully  comprehend that, had He not revealed Himself, we would not know or  understand what He is like. But, thankfully, God has not left us  ignorant about Himself. Instead, He has revealed Himself to us through  both general revelation (creation and our conscience) and special  revelation (the written Word of God, the Bible, and the living Word of  God, Jesus Christ). Therefore, we can know God, and we can know how to  be reconciled to Him and how to live according to His will. Despite the  fact that we are finite and God is infinite, we can know and understand  God as He has revealed Himself to us.