Paul urges the Corinthians not to receive God's grace and then do nothing with it. He quotes from the Old Testament, saying that now is the right time, now is the day to be saved. There is no reason to wait.
Paul then describes the many ways he and his fellow workers have proven themselves to be God's true servants. The list is long and difficult: they have been through terrible hardships, beatings, imprisonment, and sleepless nights. But they have also shown kindness, love, and honesty. They are treated as liars, but they speak the truth. They are treated as if they are dying, but they keep living. They seem to have nothing, but they actually have everything.
Paul then opens his heart to the Corinthians. He tells them that he has spoken freely and that his heart is wide open to them. The problem is not on his side, it is on theirs. He asks them to open their hearts back to him. He closes the chapter by warning them not to team up with people who do not follow God. Light and darkness do not go together. Christ and evil do not go together. God calls his people to be separate and clean. God says he will be a father to them and they will be his sons and daughters.
Historical Context
In Paul's time, Corinth was a wealthy city full of temples and idol worship. Many believers had come out of that world and were still surrounded by it every day. Some were being pulled back toward old habits and friendships that did not honor God.
Paul's warning about not being "unequally yoked" with unbelievers comes from farming. A yoke is a wooden frame put on two animals to pull a cart together. If the two animals are different sizes or types, they pull in different directions and it becomes a mess. Paul uses this picture to explain that when believers try to be deeply tied to people who want to go the opposite direction spiritually, it causes real problems.