Do not be anxious about anything, but in every situation, by prayer and petition, with thanksgiving, present your requests to God. And the peace of God, which transcends all understanding, will guard your hearts and your minds in Christ Jesus (Philippians 4:6-7).
This is the only place in Scripture that directly speaks of "the peace of God," even though there are several places that speak of "the God of peace." One might perhaps include Jesus' offer of peace to His disciples as the peace of God:
Peace I leave with you; my peace I give you. I do not give to you as the world gives. Do not let your hearts be troubled and do not be afraid (John 14:27).
I have told you these things, so that in me you may have peace. In this world you will have trouble. But take heart! I have overcome the world (John 16:33).
Paul speaks of the peace of God as that which "transcends all understanding." Jesus speaks of His peace as different from what "the world gives." Paul speaks of the peace of God as guarding hearts and minds against anxiety. Jesus speaks of His peace as encouraging troubled and fearful hearts. Both Paul and Jesus probably had persecution in view, as they both write in the context of Christians enduring persecution from the world.
The transcendant nature of "the peace of God" is parallel to the other-worldly nature of the peace that Christ offered. In other words, the origin and motivation of this peace has no earthly root. It comes from heaven. It is not bound by the finite and temporal. It is infinite and eternal, because it arises out of the believer's relationship to Jesus Christ. That is why Paul writes of the peace of God as guarding minds and hearts "in Christ Jesus."
Paul speaks of this peace as guarding their hearts and minds. As other commentators have noted, the word "guard" has a military sense and suggests a garrison of soldiers protecting a fort. This garrison would, thus, be protecting the believers' hearts and minds. The language is similar to Paul's description of the armor of God in Ephesians 6:10-17, where Paul describes each piece of armor as an aspect of the believer's secure salvation in Christ. The sense is that the believer is completely secure in Christ. Come what may, the believer can declare, "I can do all things through Him who gives me strength" (Philiippians 4:13). For this is their confidence:
If God is for us, who can be against us?He who did not spare his own Son, but gave him up for us all—how will he not also, along with him, graciously give us all things? (Romans 8:31-32).
Since God is for the believer and since God have given the believer what is most precious to Him, what does the believer have to worry about?! Nothing at all! Instead, the believer has every reason for absolute confidence in Christ:
No, in all these things we are more than conquerors through him who loved us. For I am convinced that neither death nor life, neither angels nor demons, neither the present nor the future, nor any powers, neither height nor depth, nor anything else in all creation, will be able to separate us from the love of God that is in Christ Jesus our Lord (Romans 8:37-39).
So, what is the peace of God? It is our eternal hope in Christ Jesus. It is the whole weight of glory that awaits us in heaven that makes everything else pale in comparison. It is the joy in knowing God loves us and has adopted us into His eternal family and made us coheirs with Christ in His kingdom. It is the rest in the confident assurance that God, who made all things and who sustains all things, is in control and is for us and not against us. It is this peace that transcends all understanding and guards our hearts and minds in Christ Jesus.