Paul spent about a year and a half in Corinth (AD 52-53) during the latter half of his Second Missionary Journey. He made many disciples there. During his Third Missionary Journey, he spent 3 years in Ephesus, AD 54-57. While in Ephesus, Paul wrote 1 Corinthians. Soon afterward, the great Riot occurred, in which Paul nearly lost his life (Acts 19).
Leaving Ephesus, he went to Macedonia, on his way to Corinth. While in Macedonia in the summer and fall of AD 57, he visited the churches in the region of Philippi and Thessalonica. While there, he met Titus, who was returning from Corinth with the word tht Paul's first letter had done much good (2 Cor. 7:6). However, there were still some leaders in the Corinthian Church who were denying that Paul was a Genuine Apostle of Chirst.
Because of this, Paul wrote this second letter to the church at Corinth, sending it with Titus, ahead of his visit.
Its purpose appears mainly to be Paul's vindication of himself as an Apostle of Christ, and to remind them that, since he founded the Church at Corinth, he still had the right to have a say in its management.