What does 1 Corinthians 14:16 mean?
Prayer is, by definition, spiritual communication. It takes place between a believer's spirit and God by way of God's Holy Spirit. Paul has shown in the previous verses that prayer should also involve the mind. In other words, prayer is best when the person praying knows what he or she is saying to God.That's why Paul has urged those who have the gift of tongues to ask God to give them the gift of interpretation, as well. Then, when they pray to God in an unknown language, they will know what they are saying. Otherwise, prayer is limited to a merely spiritual experience for that person.
If that prayer is being spoken in an unknown tongue in a worship service, without an interpreter present, it is even worse for those who are listening. For them, the person's prayer is neither spiritual—since they are not the one praying—or intellectual—since they don't know what is being said. It becomes meaningless.
This is why Paul writes here that nobody who hears the prayer of thanksgiving of someone speaking in tongues, without interpretation, can say "Amen." The word amen is a term of agreement and endorsement. Those who don't understand the words cannot be encouraged by the expression of thanks, and they cannot amplify it by agreeing. It becomes meaningless for them.
The word "outsider" in this verse most likely refers to everyone listening who does not understand what it being said in the unknown language.