When we say "Peace be with you" we are wishing the blessing of the fullness of peace upon the person to whom we are speaking. We are vocalizing a prayer to God that every good thing might come to that person.
In my home office I have a mounted sheet of wrapping paper that I purchased at Ten Thousand Villages. It is in the color of Advent blue with international words for peace written on it including kalinaw, pax, hoa binh, peace, nabad, dawa, amani, and a variety of words written in global characters that spell out shalom, salam... These words don't simply mean the absence of war or fighting (armistice), but the fullfillment of perfect peace - health, healing, wholeness in body, mind, spirit, relationships, community, ecological harmony, total restoration and love. In our Christian tradition we better understand the concept of this fullness of peace by resting ever deeper in Christ's perfect love perfecting us and all creation across time and space.
By grace (in relationship, baptism, communion...) the view of Jesus as prince of armistice fades. Through the lens of faith, the view of Jesus the Prince of Peace becomes clearer.
To learn more, search for how and where the word peace is used throughout the Bible using a resource called a lexicon such as at http://www.biblestudytools.com/lexicons/hebrew/kjv/shalam.html. You can see by the hyperlink that I have looked up the Hebrew word "shalam" (peace) in the King James Version (kjv) lexicon. The King James Version uses the English language in a different way than the New Revised Standard Version (NRSV) of the Bible. Use this internet site to explore a variety of Bible translations and texts to gain new insights. This kind of word searching is "spirited discipleship." Thanks be to God.
Pr. Karen Kuhnert