Philippians 4:7

Majority Text:
και η ειρήνη του Θεου η υπερέχουσα πάντα νουν φρουρήσει τας καρδίας υμων και τα νοήματα υμων εν Χριστω ᾿Ιησου.

KJV:
And the peace of God, which passeth all understanding, shall keep your hearts and minds through Christ Jesus.

Comments:
the peace of God: Interestingly, Paul mentions the God of peace only two verses below, in verse 9. His point there is not really very distinct from the point here--with the exception that he changes the emphasis from peace to God. That is, the point in this verse is that when believers trust God, He blesses them with a certain kind of peace. In that verse, when believers are living obediently they are blessed with the presence of God (who happens to bring peace with Him).

which passeth all understanding: When turmoil ends there is peace. When a problem finds resolution there is peace. But this peace is more than that. The peace God provides is not simply a resolution of the conflict. It has the added dimension of confidence and hope that comes from realizing that the resolution came from One who is faithful to provide in all circumstances--the point of the peace leading also through tribulation to hope in Romans 5:1-5.

Expanded Paraphrase:
When you learn to depend on God for the things about which you would otherwise worry, you put yourself in a position to receive both real resolution to your conflicts and the attendant comfort and confidence that come with that resolution. But you receive from God a peace outside the bounds of human provision, because neither you nor any other fallible man provided it. God addresses your need. And because God addresses your need you find permanent peace in your growing awareness of His faithfulness--a peace no one unaware of God's provision comprehends.