Simply, this is a period of time in which God exclusively deals with a corporate group He has called and chosen as His people, giving them responsibility for the care of His testimony and His glory in the earth. God looks for obedience to His will and unity by the group in this representation. Only two callings of corporate groups ever existed in the Bible: that of the nation of Israel and that of the church, the body of Christ.
For a detailed explanation on “dispensations”, click here:
This link explains how the Bible shows the transition from the first dispensation to the second:
This article explains more on the transition but focuses on what it means to say Israel was set aside: