What does 1 Corinthians 9:4 mean?

Paul asks a series of questions about his right as one of the apostles. He begins with asking if he and other apostles have a right to eat and drink. By this, he means they have a right to have their necessities met, starting with the most basic of all, food and drink.

Paul is leading up to the idea that, as a minister of the gospel—and especially as an apostle—he could ask those he serves to provide him support so he would not have to work outside of ministry to support himself. Then, he will remind the Corinthians that he has never asked them to do this. His reason for making this comparison is to show that Paul practices what he preaches. He has asked the believers in Corinth to put their "rights" aside for the good of others, which is something Paul himself has already demonstrated.