What does 1 Corinthians 16:4 mean?

This verse wraps up Paul's instructions to the Corinthians about how to arrange relief for suffering Jewish Christians in Jerusalem. He has told them to set aside money, week by week, in proportion to their income, as well as to designate some from among them to deliver the money to Jerusalem.

Paul appears to be carefully planning the operation to avoid any accusations he might take the money for himself. Not only does he insist that a delegation from the church should deliver the gift, he now shows that he is willing to allow the Corinthians to decide if he should make the trip with them or not.

Paul could, of course, have asserted his authority as an apostle to deliver the money himself or, at least, to accompany the group. Instead, he allows the greatest possible freedom to the Corinthians, ensuring that this gift is given willingly by them out of a spirit of generosity and not out of grudging obedience to Paul's perceived arm-twisting. This fits with what he will write to them in his next letter, "Each one must give as he has decided in his heart, not reluctantly or under compulsion, for God loves a cheerful giver" (2 Corinthians 9:7).