This boasting reaches its climax in chapter 12. There Paul says he knows a man (a roundabout way of talking about himself) who 14 years prior to the writing of this letter was caught up into the third heaven, into paradise, and heard things so majestic that he can not repeat them. This is exactly the kind of thing the the Corinthians have been looking for all along. We can gather from 1 Corinthians that this church was one which highly prized rapturous spiritual experiences. In that letter, Paul is constantly reminding them that the real mark of the Spirit's presence among them is not showy, ethereal experiences like speaking in tongues but the ordinary, every day task of loving each other. It seems that because the Corinthians were having these great spiritual experiences and Paul never talked about having any such experiences of his own, the Corinthians began to believe they might actually be more spiritual than the apostle who brought them the gospel in the first place. In spite of these accusations and the tension that runs through the Corinthian correspondence, Paul refused to reveal that he had exactly the kind of visions which the Corinthians valued so highly - until now.
But even here, in his boasting, Paul turns the discussion back to weakness. He gives into the Corinthians demands just for a moment to let them know that he has a whole life of spiritual experiences that he has not boasted to them about because he doesn't believe those experiences are what make him an apostle. Rather it is imitating the weakness and vulnerability of his Lord which makes him a true messenger of the good news. So Paul says he will rather boast in his weakness.
Specifically, Paul speaks of his weakness as a "thorn in the flesh". He doesn't tell us exactly what this thorn was (see commentaries for endless speculation: sexual temptation, being small of stature, persecutions, weak public speaker, some other physical or even mental illness) but he does tell us that it was given to him to keep him from becoming conceited because of the greatness of his revelations and visions. Contrary to the Corinthians opinion, Paul's spiritual experiences are actually so extraordinary that he needed an affliction of some kind just to check his ego.
Even more remarkably, the great Apostle Paul asked God on three separate occasions to take away this thorn and his request was never granted. Instead, Christ responded by saying "My grace is sufficient for you, for my power is made perfect in weakness." Paul concludes this paragraph by saying
"Therefore I will boast all the more gladly of my weaknesses, so that the power of Christ may rest upon me. 10For the sake of Christ, then, I am content with weaknesses, insults, hardships, persecutions, and calamities. For when I am weak, then I am strong."This is not a pithy little word of encouragement destined for a refrigerator magnet to remind us that God is still with us even though we are having a crappy day. It is fundamental to Paul's understanding of Jesus and his own ministry as one of Jesus' ambassadors. It is a foundational conviction of Paul's post-road-to-Damascus life that when God wanted to demonstrate his world-changing, reality-altering strength he did it through the weakness and vulnerability of his Christ hung on a Roman instrument of execution. Likewise, as followers of this Messiah we are meant to imitate his example. It is not that this powerful God merely happens to be with us in our weakness, true and important though that is. It is that Christ reveals to us that God's very way is weakness. It is not something God merely tolerates but something God chooses. That for all the glory and might of the Triune God, there is eternally and permanently weakness within the life of this God as well and in the upside down kingdom which Christ establishes weakness is actually strength.
We often think of weaknesses as obstacles to ministry. We don't have enough money or space or people in our church to do certain things. The people who are here feel like they can't contribute because they are too old and their bodies ache too much. And so we pray repeatedly for God to bless us. And we should. But after we've offered that prayer a number of times and the blessing we are seeking hasn't come maybe we should begin to consider that our very real weaknesses are not obstacles to ministry but the very means by which God intends for us to minister. So that we might imitate and embody the weakness of our savior. So that God's power might be displayed instead of ours. So that we may lean forward into the coming kingdom of our crucified and risen Lord.