What does 2 Corinthians 13:6 mean?

In the previous verse, Paul asked the Corinthians to test themselves to see that Jesus Christ is in them. In this context, he apparently assumes the answer will be that Christ is, truly, living within them, despite their flaws and errors. If that is their answer, Paul and his associates will have passed a test, as well. That would imply they are genuine in representing Christ. Paul is the one who introduced them to Christ. If Christ is real and genuine to them and in them, they must acknowledge that Christ is also in Paul and speaking through him.

The logic of that relationship continues, however. If Christ is speaking through Paul, the Corinthian believers must prepare to be judged by Christ, through Paul, for any unrepentant sin in their lives. They must acknowledge Paul's authority as an apostle.

Another layer of meaning here would be that if Christ is truly in them, the Corinthians should know to repent of sin and move away from it, in order to avoid Christ's discipline through Paul.