Because of the work Paul and his companions had done, the world could look at the Corinthians and see how Christ blesses people in this life. Some modern translations read, "delivered by us."
"It was written not with ink but it was written by the Spirit of the living God" or "It is not a letter that people wrote with ink but a letter that the Spirit of the living God wrote"
Paul speaks of their hearts as if they are flat pieces of stone or clay upon which people engraved letters. Paul alludes to God giving the Ten Commandments on stone tablets. This represents the law of Moses. The law was good because it came from God. But God punished the Israelites because they disobeyed it.