There are only a few references to singing in the New Testament. Jesus and the disciple sang a hymn before the crucifixion (Matthew 26). Paul and Silas sang hymns of praise in jail (Acts 16).
In addition there are two passages that give teaching about the purpose of singing.
Therefore be careful how you walk, not as unwise men but as wise, making the most of your time, because the days are evil. So then do not be foolish, but understand what the will of the Lord is. And do not get drunk with wine, for that is dissipation, but be filled with the Spirit, speaking to one another in psalms and hymns and spiritual songs, singing and making melody with your heart to the Lord; always giving thanks for all things in the name of our Lord Jesus Christ to God, even the Father; and be subject to one another in the fear of Christ.
Let the word of Christ richly dwell within you, with all wisdom teaching and admonishing one another with psalms and hymns and spiritual songs, singing with thankfulness in your hearts to God. Whatever you do in word or deed, do all in the name of the Lord Jesus, giving thanks through Him to God the Father.
Listing the details of singing in these verses:
- speaking to one another
- making melody with your heart
- teaching and admonishing one another
- being thankful to God
This gives me the impression the purpose of songs is to help each other – teaching and admonishing (warning). Combine this with the instruction in 1 Corinthians 14:26 that everything we do is for edification (building up). Songs are a way we can help other Christians to live the Christian life.
As a side note, what these teaching passages do not say is that the purpose of singing is to worship God.