During the Renaissance when printing was a relatively new technology and had potentially revolutionary implications about access to and flow of ideas, most European states had some form of prior censorship in place. Although there were clandestine printers and publications (for example, Catholics in England did publish propaganda of various kinds that was not officially approved by the English government), most printers had to have things they printed approved first by some governmental body. The Roman Church, which has since the late Roman period tended to operate like a state. had its censorship apparatus. People subject to Roman Catholic authorities, if they wished to publish, had to submit what they intended to publish to Church aurthorities. Some delegate of the authority, a censor librorum would read the thing, and if he found nothing objectionable, would send it up to the higher authority with a declaration, Nihil obstat. Nothing stands in the way. The hgher authority might then review it and issue an Imprimatur, Let it be printed.
Nowadays, this is not very much operative, although regular and secular clergy, who are, at least in theory, more closely controlled, may have to submit to some such process.
But the era of the Renaissance is over. We live in an era where ideas circulate more freely. Catholics too are able to participate in the commerce of ideas in a full and expansive way. Some clerical types, especially some of those running about in the corridors of the Vatican, would like to push back the clock. But they are fighting a losing battle. Freedom of thought is here to stay, for Catholics too.!