Overspel is the Dutch word for adultery. Depending on the period, adultery was not only a private matter, but could be criminally prosecuted. The church council also wanted to find out so that both parties could be censored.
One of my own female ancestors was fined for insulting another woman, saying “You are keeping company with my man” and other more derogatory terms. As far as I know, the husband or the woman he was having an affair with were never prosecuted. Stories like these sure help to understand where all those strange DNA matches come from!