Peace according to Webster dictionary is freedom from agitation or disturbance by the passions, as from fear, terror, anger, anxiety or the like; quietness of mind; tranquillity; calmness; quiet of conscience.
Isaiah 26:3 says, You will keep him in perfect peace, Whose mind is stayed on You, Because he trusts in You.
When we trust (hope confidently) in God, our minds will be focused on Him and the result will be peace in our lives.
Psalm 119:165 says, Great peace have those who love Your law, And nothing causes them to stumble.
Great calmness of mind is as a result of loving the Word of God. These people put the Word of God first, which leads to them having peace and hence they do not fall into sin; they are kept safe; they are preserved from the power of temptation.
John 14:27 says, Peace I leave with you, My peace I give to you; not as the world gives do I give to you. Let not your heart be troubled, neither let it be afraid.
Jesus was consoling His disciples in view of his approaching death. He was giving them a blessing of peace. Jesus’ own peace, not as the objects which men commonly pursue – pleasure, fame, wealth. These do not meet the desires of the immortal mind, and they are incapable of affording that peace which the soul needs. Jesus’ peace is such as meets all the wants of the soul, silences the alarms of conscience, is fixed and sure amid all external changes. Jesus encouraged His disciples not to let their hearts be afraid of any pain, persecutions, or trials. We also have a Friend who will never leave us; we have a peace that shall always attend to us.
And finally, Philippians 4:6 – 7 Be anxious for nothing, 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 minds through Christ Jesus.
With focus on verse 7, the peace referred to here is that which is felt when we have no anxious care about the supply of our needs, and when we go confidently and commit everything into the hands of God. This kind of peace surpasses all that people can imagine. When we make our requests known to God, and go to him in view of all our trials and wants, the mind is preserved from distressing anxiety. Go and spread out all before the Lord. The peace of God will guard (shall keep), “shall keep” is a military term, and means that the mind would be guarded as a camp or castle is. It would be preserved from the intrusion of anxious fears and alarms.
It is only in Jesus that the mind can be preserved in peace.