What does 2 Corinthians 10:18 mean?

The bottom line of this passage is that Paul does not need to compete in a bragging contest with opponents in Corinth. Those false teachers may have been skillful by the standards of the day: demonstrating superiority through speaking skill, self-promotion, and tearing down competitors. Commending oneself was an important part of that competition.

Paul has said that he refuses to participate in that competition for several reasons. First, he has already accomplished what he set out to do: leading the Corinthians to faith in Christ. Another reason is that praising oneself does not actually make the person who is boasting worthy of anything. The self-praiser is not approved by anyone except himself. The one who is commended by the Lord, though, is approved by the one who matters most.

Paul is urging the Corinthians to stop allowing shallow showmen to turn their minds away from Paul and, by implication, away from Christ. They should know, better than most, that Paul's role as Christ's representative is genuine. They believed in Christ because of Paul's message. At least for that reason, they should know the Lord has commended Paul. God's approval of Paul should be the only opinion that matters to them.