It's the excommunication from the congregation by Paul.
I don't find that term used, but I do assume that discipline was administered and the offending party was sent out. However, that really doesn't explain why Paul spent so much time preaching to the Corinthians about their own spiritual maturity, while not even mentioning the name of the unrepentant one. (
"I do not write these things to shame you, but to admonish you as my beloved children.")
I think to focus on the obvious sin of the man is to miss the greater lesson to all believers. ("Do you not judge those who are within the church?....REMOVE THE WICKED MAN FROM AMONG YOURSELVES.")