Examine yourselves, to see whether you are in the faith. Test yourselves. Or do you not realize this about yourselves, that Jesus Christ is in you?—unless indeed you fail to meet the test!—2 Corinthians 13:5 (ESV)
True conversion from death to life results in the power of God, through the Holy Spirit, working in us to transform our lives. Our old selves have been put to death, and behold we have been recreated spiritually and are being recreated from the inside out. Our thoughts and our passions are being renewed by the spirit of God so that they are pleasing to Him. We also learn to deal with sinful thoughts and passions, often influenced by our emotions, in a way that pleases God and demonstrates love and grace toward others. In short, these inner changes produce outward changes in the person who has been truly reborn into the family of God.
Why did Paul implore them to test themselves? It seems as though many in the Corinthian church were still committing sexual sins with no sign of a change of mind. Sure, some sins are not easy to overcome, but I think Paul’s biggest concern was that many of them seemed to have little concern over their sexual immorality (see 2 Cor. 12:20-21). They had not decided that they were really sinning against the Holy God. I think Paul’s concern was that they had knowledge of the gospel (1 Cor. 1:5-6), but they had not really applied faith to truly believe or trust in Jesus for salvation.
One can understand facts, like water freezes and becomes slippery on roads or like the death and resurrection of Christ, but when one truly believes in these facts, when he bets his life on them being true, they affect the way he lives. In the former example, he drives much more carefully or uses chains on his tires, and in the latter example, he forsakes and changes his mind (on some level) regarding his love for the evil things of the world and loves God. As he loves God more, his discernment of good versus evil is more accurate, and he loves God more and hates what is sinful more (see Philip. 1:9-10).
Of course a man can not judge another man’s faith. A man can only judge outward appearances. This is why Paul said examine and test “yourselves,” not “each other.” John’s letters (1, 2, 3 John) also communicate very similar ideas.
If there is one thing that I have seen over and over that hinders many from salvation (or at least demonstrating any fruit of salvation), it is their sexual behavior. At some point they realize they have to condemn their own behavior or change what they believe about God. Sadly, many choose the latter, and many so-called Christians (see 1 Cor. 5:11) twist or misinterpret the Old and New Testament to justify their behavior.
Paul was not merely interested in carrying out church discipline on these individuals, he was really interested in their spiritual welfare and edification and more generally, these of the Corinthian church (see 2 Cor. 13:9-11). Therefore, our response to this should be to do the same.