Abraham became a stranger when he entered a strange (although promised) land. But most Christians become strangers in their own country when they come to Christ. You start to act different and you confess that your home is with the Lord. This is emphasized in the letters of Peter (1 Peter 1:1 and 1 Peter 2:11).
13 These all died in faith, not having received the things promised, but having seen them and greeted them from afar, and having acknowledged that they were strangers and exiles on the earth.