What does 1 Corinthians 9:3 mean?

In the previous two verses, Paul established that he is a true apostle of Jesus Christ. "Apostle," in this case, means one specially sent by Christ as a messenger to others. The Corinthians are fully aware that Paul came to them in exactly this way. They exist as a community of Christians because they believed the message of Jesus as he presented it to them.

Now Paul reports that what follows will be his defense before those who will examine him. In other words, he is about to present arguments about himself, arguments he believes will hold up to scrutiny.

What will Paul be defending? He plans to show that, as an apostle, he has rights to several things. Among those is the right to be supported financially by those he serves with the gospel. And yet, Paul will also argue that he has not demanded those rights, out of love and concern for those to whom he ministers. He means this as an example of how Christians ought to put their "rights" secondary to the spiritual good of others.