Don

I have no idea what “declaring someone is bound to their sin” means.

To bind is to forbid some act and to loose is to permit some act, as a Jewish idiom used in the Mishnah.  At the Jerusalem council the disciples decided that gentiles did not need to be circumcized (that is, become Jews) and could remain gentiles, but please do not do these 4 things that disturb Jewish sensitivities.  So they loosed the need for conversion to Judaism and bound the 4 things.