God is omnipotent. But that doesn’t mean God can do _anything_ at all. In fact, there are several things God cannot do. Omnipotence means _nothing is too hard for God_.
Jeremiah 32:17, 27 contains the following exchange:
“Ah Lord God! Behold, You have made the heavens and the earth by Your great power and by Your outstretched arm! Nothing is too difficult for you,” … “Behold, I am the LORD, the God of all flesh; is anything too difficult for Me?”
God can also do more than we can imagine:
Ephesians 3:20 Now to Him who is able to do far more abundantly beyond all that we ask or think…
On the other hand, if you asked God what my imaginary childhood friend looked like, He’d have no answer because that person never existed. Similarly, God cannot find the corner of a circle, as that is illogical. Nor can God create a rock so big He can’t lift it. That’s not too hard for Him, it’s just illogical. Such a rock cannot logically exist. It’s like asking “what happens when an irresistible force meets an immovable object?” By definition, only one of those entities can exist at one time within the universe. The existence of one denies the existence of the other. The existence of an immovable rock denies the existence of an omnipotent God. That rock does not, and cannot exist. So it’s a silly question.
God also cannot do certain things which violate His will and character.
Hebrews 6:18 – so that by two unchangeable things in which _it is impossible for God to lie_, we who have taken refuge would have strongb encouragement to take hold of the hope set before us.
2 Timothy 2:13 – If we are faithless, He remains faithful, for _He cannot deny Himself_.
(All scripture NASB. Emphasis added)
The fact that these things are impossible for God should actually be a source of great comfort to those who love Him. It doesn’t mean He’s less than omnipotent. It means He is _trustworthy_. Man can lie. God cannot. Which is more perfect?
The fact that nothing is too difficult for God means we can trust that He is _capable_ of keeping that which we’ve committed to Him. He’s strong enough to rescue us from any danger, and strong enough to keep His promises. The fact that it is impossible for God to act against His character means we can trust that He _will_ keep those promises to His children.
[From my systematic theology class.]