Peace of God is that rest, calmness and that sense of quietness that God gives to His children. It is that comfort He gives to them even in the midst of trials and afflictions.
In reacting to this, Jesus began to say:
John 14:27 KJV
Peace I leave with you, my peace I give unto you: not as the world giveth, give I unto you. Let not your heart be troubled, neither let it be afraid.
Peace Received and Peace Given
We have said the peace of God is received at the instance of the Holy Spirit. That is to say, when we receive the Comforter (the Holy Spirit), then; we have received comfort or the peace of God.
However, to live in comfort or peace with yourself is more than having the Comforter which is the Holy Spirit This is where activating the peace of God comes in.
See, there is a nexus between the gift of peace and the fruit of peace, both from the Spirit. The point being made is that the gift of the Holy Spirit equals the gift of peace; however, for that peace to flow ceaselessly upon you, then you need to develop it.