Paul's first letter to the Christians at Corinth was pretty harsh, and rightly so--the Corinthian church was plagued by division, lawsuits, and open sinfulness and they needed to be called out for some of their major issues. But now in his second letter to the Corinthians, Paul is offering some comfort. Paul also addresses some rumors and accusations against himself from people who say that he is lacking as an apostle and is unqualified to preach.
After the initial greetings in chapter one, Paul presents a contrast between consolation and suffering, mentioning that God "comforteth us in all our tribulation, that we may be able to comfort them which are in any trouble, by the comfort wherewith we ourselves are comforted of God. For as the sufferings of Christ abound in us, so our consolation also aboundeth by Christ" (1:4-5). There's no denying that there's an element of suffering involved in being a follower of Christ. Jesus himself endured the ultimate suffering, so people who love him can't expect to avoid hardship entirely. However, Paul is discussing the immense spiritual comfort that God provides whenever we are experiencing trouble. Paul goes on to discuss his own tribulations and to thank the Corinthian church for praying for him and for his fellow ministers.
Paul also explains the reasons for the severity of his last letter: "For out of much affliction and anguish of heart I wrote unto you with many tears; not that ye should be grieved, but that ye might know the love which I have more abundantly unto you." In other words, he wasn't trying to berate them or emotionally destroy them, but he was speaking in a stern manner because of how much he loved them and was worried about their behavior. One particular case of sinfulness that Paul pointed out in 1st Corinthians is addressed again, and Paul says that now that the man has repented of his wrongdoings, the Corinthians should comfort him and express their love for him.
Chapter 4 shows some more of the suffering/consolation paradox, when Paul speaks of himself and of other ministers of the gospel: "We are troubled on every side, yet not distressed; we are perplexed, but not in despair; Persecuted, but not forsaken; cast down, but not destroyed" (4:8-9). They never give up because they are working toward an eternal goal, and the rewards are far greater than the price they pay: "For our light affliction, which is but for a moment, worketh for us a far more exceeding and eternal weight of glory"(4:17).
2nd Corinthians also has some very personal discussions from Paul, where he talks about things in his own life that he doesn't mention (or rarely mentions) elsewhere in the letters he writes. For one thing, chapter 12 mentions some kind of physical malady that Paul has, which the Lord has decided not to heal. Some people guess that Paul had a problem with his eyes, but the exact nature of his "thorn in the flesh" is never described. Paul ends his letter by saying that he's about to come and visit the Corinthians for a third time, and I like how this shows that he had an ongoing relationship with their church. He concludes with some encouraging words: "Finally, brethren, farewell. Be perfect, be of good comfort, be of one mind, live in peace; and the God of love and peace shall be with you" (13:11).