And the peace of God, which surpasses all understanding, will guard your hearts and your minds in Christ Jesus. (ESV)
In the previous verse Paul admonished the Philippian believers, and you and I, to give our anxiety to the Lord. When anxiety comes the believer is to go to the Lord in prayer, with thanksgiving, recognizing that God alone is the one who can overcome all that would instill fear in our hearts. He now shows us the result of bringing our cares and anxieties to the Lord.
God's peace is given to his children to guard them. It is important to note that this peace is not a worldly peace. Those who do not know the Lord can talk about peace all they want, but they will never know true peace until they know the true source of peace. It is no small wonder that one of the many divine titles of Jesus is "Prince of Peace." (Isaiah 9:6)
Those who do not know the Lord can prescribe pills to alleviate anxiety. But they will not guard hearts and minds like the peace of God. Nations can provide a military solution and even eliminate the threat of enemies attacking. But that peace is not the same as what Jesus offers. We can even possess all of the things that we think a person could need or want. That will not give us peace.
If you are a believer in Jesus Christ, true peace is for you. If you lack peace go to the Prince of Peace in prayer. Bring him all of the fears and anxieties that are crippling you. Thank him in advance for the peace he will provide and ask him to give you his peace. Our wonderful savior is faithful. He will not turn you away. I leave you with the Savior's words:
 Peace I leave with you; my peace I give to you. Not as the world gives do I give to you. Let not your hearts be troubled, neither let them be afraid. (ESV)