The Peace of God

   The first thing you need to know about the peace of God is that you do not earn or struggle for it.  It's not hard won.  The peace of God is given, and even then, when you've received it, you won't understand why it does what it does.  Here's what Paul says:

[D]o not be anxious about anything, but in everything by prayer and supplication with thanksgiving let your requests be made known to God.  And the peace of God, which surpasses all understanding, will guard your hearts and your minds in Christ Jesus.    (Philippians 4:6-7, ESV)

   Part of the reason you won't understand it is because it is spiritual: it comes from the Spirit of God.  Just like we don't understand with our minds just what is being said when we pray in the Spirit, we don't understand with our minds what is happening to our Souls when the peace of God is at work.  And because the peace of God is spiritual, you can't do something physical to obtain it.  That's why you pray for it; again, a spiritual thing.
   Now as to why the peace of God is important, Paul tells us that as well, and it's because His peace guards our hearts and minds.  And from what are our hearts and minds guarded?  From anxiety for starters.  That's what Paul is directly answering here in his letter, what to do if we feel anxious.  Wrapped up in anxiety is also everything else that keeps unpeaceful: worry, fear, and the attempts to sculpt our future.  Anxiety I think encompasses all of this.  The word "anxious" is defined three ways by Merriam-Webster:

1) characterized by extreme uneasiness of mind or brooding fear about some contingency (worried);
2) characterized by, resulting from, or causing anxiety; and
3) ardently or earnestly wishing.

   What is interesting is that the word anxious is not defined in entirely negative terms.  The third definition isn't inherently negative, but from the perspective of wanting peace it is.  The effort we put into wishing for something to happen detracts from the attention we give to life as it is.  The less we appreciate life as it is, the less peace we usually have, because we're anxious to have an "improved" or simply "different" life.  The peace of God can guard us from this state of mind, this state of heart.  The peace of God is here in the words of Jesus: "Therefore do not be anxious about tomorrow, for tomorrow will be anxious for itself. Sufficient for the day is its own trouble." (Matthew 6:34, ESV)