Apphia was a wife of Philemon. She, her husband Philemon, Archippus, and the church that met in their house were the recipients of Paul's Epistle to Philemon.
To Philemon our dearly beloved friend and fellow worker, and to [your wife] Apphia our sister, and to Archippus our fellow soldier [in ministry], and to the church that meets in your house: Grace to you and peace [inner calm and spiritual well-being] from God our Father and the Lord Jesus Christ.— Philemon 1:1 (AMP)
Paul prayed for them due to their love and faith in God and their fellow Christians.
I thank my God always, making mention of you in my prayers, because I hear of your love and of your faith which you have toward the Lord Jesus and toward all the saints (God’s people). I pray that the sharing of your faith may become effective and powerful because of your accurate knowledge of every good thing which is ours in Christ. For I have had great joy and comfort and encouragement from your love, because the hearts of the saints (God’s people) have been refreshed through you, my brother.— Philemon 1:4–1:7 (AMP)
Paul sent Onesimus to them and asked them to accept and forgive Onesimus, who Paul had converted to Christianity. Paul asked them for permission to have Onesimus minister to him on the behalf of Philemon and his household. Paul also asked them to prepare a room for Paul in case he is allowed to visit.