It's more than just a greeting. When we say "Shabbat Shalom," we are actually conferring a blessing for peace upon one another. This audio teaching, tangentially related to parashat Tzav, explores the concept of the Sabbath peace with reference to Yeshua's instructions:
When you come to the house, ask of it’s shalom. It will be that if the house is worthy, your shalom will come upon it, and if it is not worthy, your shalom will return to you. (Matthew 10:12)