Q. 1. What does the word "anathema" mean in the Catholic Church. I noticed that in some Catholic documents it says "Let him be anathema."
A. 1. When the Catholic Church says, "Let him be anathema," it means "Let him be excommunicated." The following paragraph from the Catechism of the Catholic Church explains the application of anathema/excommunication.
"Certain particularly grave sins incur excommunication, the most severe ecclesiastical penalty, which impedes the reception of the sacraments and the exercise of certain ecclesiastical acts, and for which absolution consequently cannot be granted, according to canon law, except by the Pope, the bishop of the place or priests authorized by them. In danger of death any priest, even if deprived of faculties for hearing confessions, can absolve from every sin and excommunication." [Catechism of the Catholic Church # 1463]
An excommunication is usually applied when someone promotes false teachings in the name of the Catholic Church. This severe penalty invites the person who erred to reconsider his position.