This is one of those major promises of God that has sustained, comforted, encouraged, and strengthened so many Christians down through the years. And most are aware this verse is tied forever with the previous word from God's Spirit through the pen of the apostle Paul. We are told by Paul that we need not be anxious for anything, but we should take everything, especially those things that seem to cause anxiety in our hearts, and we are to prayerfully supplicate these matters to our Heavenly Father, and do so with thanksgiving.
I've always appreciated the words in verse 6, "...let your requests be made known unto God." God already knows, but He wants us to place these matters in His hands and leave them there. As a result, God places in our hearts a peace that we just can't explain because it is a peace that "surpasses all understanding"!
For every time your heart gets anxious, whether it be for a very real issue you're facing, or even if it is accusations against your life by the devil, (remember, he is seen as the "adversary" who "accuses the brethren"), just take these thoughts and bring them to your Savior. And, if Jesus is your Savior, you know without a doubt His blood has cleansed you from every sin. If the anxiety is an issue seemingly insurmountable to you, then remember Christ is your strength and He will do what is impossible for you to do.
Peace is given to us by Jesus. Read John 14:27. Memorize it and meditate on it. It is a companion verse to our Daily Verse of today. God wants you to enjoy His peace! That peace in your heart stands like a security guard protecting your heart and mind. That includes your emotions and your thoughts. Too many Christians are troubled today and need not be if they would give their worries, concerns, and cares over to their Savior.
May you enjoy the peace that surpasses all understanding today!