All the saints greet you, especially those of Caesar's household. (ESV)
We live in a very mobile world. One hundred years ago it was very likely that during your lifetime you never left the state that you were born in. Sure, there was travel, but there was not as many kinds of travel accessible to the every day person. Whether by plane, train, or automobile we can be anywhere in this country in a relatively short time, and for a small cost.
If you have had the privilege of going to another part of the country and gathering together with people you have never met who love Jesus you will discover something wonderful. You have an immediate bond because of your relationship with Jesus Christ. This is something that the world cannot duplicate. The love of Christ turns strangers into friends.
Paul is sending a greeting from all the saints there with him in Rome. I am sure that very few people in Philippi knew personally many of those saints that Paul was referring to. Yet, even though great distance separated them they all shared that same wonderful bond that comes from belonging to the family of God, through Christ Jesus.
In the last phrase of this verse Paul references those of Caesar's household. The Gospel had penetrated every kind of land and every kind of people group. Caesar's own household had believers in Jesus Christ. In fact, some of the very ones who were chained to Paul in his arrest had heard the message of the Gospel of Jesus Christ. Paul sends greetings from saints, all kinds of saints. That is all a result of the wonderful love of God.
You have many wonderful friends that you have yet to meet. The bond of Christ unites you with every saint in the world and throughout history. In Heaven this bond will be fully realized. Praise God for his amazing love.