Paul was working in Macedonia, which was north from the country called Greece now. Corinth was a city in Achaia (the south part of Greece). We think that Paul wrote this letter about AD 55. That was about 25 years after Jesus died. Something was wrong among the Christians at Corinth. Some people there had been doing very wrong things. See 2 Corinthians 2:5; 12:21. Also, some of the Christians there had been listening to false teachers. See 2 Corinthians 11:4. Some of the Christians at Corinth were saying that Paul was not really Christ's servant. See 2 Corinthians 13:3.
Paul had written to the people at Corinth before and he had visited there twice. Before he wrote this letter, Paul had met his friend Titus again. Titus had just returned from a visit to the Christians at Corinth, and he told Paul good news about them. See 2 Corinthians 7:5-7. So, Paul wrote this letter to say how happy he was to hear this good news. He explains also that he really is working on Christ's behalf. And he says that he will visit Corinth again soon. He does not want to be angry with the Christians there. But he will be angry with anyone who is still not ready to put right any wrong things.