1 Corinthians 16:19

The churches of Asia salute you. Aquila and Priscilla salute you much in the Lord, with the church that is in their house (KJV)

Then: Corinthians know that Paul is near the end of his remarks. These are extra greetings from people the Corinthians would know and not know. He specifically mentions Priscilla and Aquila because of their name recognition. By adding in the fact that these two have church meetings in their home, Paul brings in a bond of familiarty with the Corinthians who do the same thing.

Now: In closing personal letters, many writers will add notes of friendship and greetings from another ".... sends his love" or ".... asked to be remembered." The purpose is to keep the bonds of love and friendship strong and active. Now, of course, it's not a usual church-to-church kind of event. Communcations and church work have changed so much that greetings are personal between minister and minister, leader and leader. The rest of the church is slightly aware of membership in fellow churches, but rarely on a personal basis.