Let not your hearts be troubled

What Jesus is saying here is "My peace I give to you." In the natural man's inner being, there is no peace. Strife is characteristic of man apart from Christ. But Jesus says come unto me all who are burdened and heavey laden and I will give you rest. Take upon my yoke because my ways are easy and my burden light. This is why we have peace. It is because we have come to a point where we can "rest in the Lord" because the battle is not our's, but the Lord's.