J.I. Packer gives the answer in his book Knowing God:
Too often the peace of God is thought of as if it were essentially a feeling of inner tranquility, happy and carefree, springing from knowledge that God will shield one from life’s hardest knocks. But this is a misrepresentation, for on the one hand, God does not featherbed his children in this way, and anyone who thinks he does is in for a shock, and on the other hand, that which is basic and essential to the real peace of God does not come into this concept at all…
The peace of God is first and foremost peace with God; it is the state of affairs in which God, instead of being against us, is for us. No account of God’s peace which does not start here can do other than mislead. One of the miserable ironies of our time is that whereas liberal and radical theologians believe themselves to be restating the gospel for today, they have for the most part rejected the categories of wrath, guilt, condemnation and the enmity of God, and so have made it impossible for themselves ever to present the gospel at all, for they cannot now state the basic problem which the gospel of peace solves.
This has application for when we pray for people, especially. How many times have you prayed for someone who is not even a Christian, “Lord, give them peace.” I’ll raise my hand on that one. What kind of peace are we praying for? in a situation? with a friend? It’s impossible for them to experience any kind of peace, as Packer points out, unless they have peace with God himself.
The only way for anyone to have that peace is to receive Jesus as their substitute Savior — as the one who took their place on the cross in order to satisfy God’s wrath against sin. When sin, condemnation, and guilt are out of the way, a river of peace will rush in and overwhelm the most weary of souls.