What does 1 Corinthians 16:3 mean?

Paul is giving the Corinthians' instructions about a collection campaign he is organizing with many of the churches he serves. They are raising funds for the Jewish Christians in Jerusalem who are living in poverty, due in part to persecution for their faith in Christ.

Paul has told them how to collect the funds in the previous verse. Now he tells them how to prepare for the delivery of the funds. He appears to have arranged delivery of the money in such a way as to ensure the highest integrity. He wants to leave no room for an accusation that he, Paul, is running a scam to take some or all of the money for himself.

For that reason, he plans to send a delegation from the Corinthian church to Jerusalem to deliver the money personally. Paul wants them to prepare for this by selecting from among themselves a group they will "accredit by letter." That is, the church will give a letter to this group to show they are official representatives delivering a gift on behalf of all their members in Corinth.

In addition to demonstrating that Paul intends to never even touch the money that has been collected, this will serve the purpose of allowing these Gentile believers to meet their Jewish counterparts in person. It will also allow the Jewish Christians to receive these moneys as a gift from their Gentile siblings and not from Paul. Very likely, Paul hopes for this moment to provide healing between these two divided groups of Christians.