[comex]

"The censor was a magistrate in ancient Rome who was responsible for maintaining the census, supervising public morality, and overseeing certain aspects of the government's finances."

https://en.wikipedia.org/wiki/Roman_censor

The name of the Roman office was based on "censere" but had a more specific meaning, and it's that which evolved into the English word "censor", due to the "supervising public morality" part of the censors' job. But the meaning shifted in the process. The Roman censors didn't "censor" anything in the modern sense; rather, they judged people for violations of public morality.

[dragonwriter]

The modern English sense of “censor”, IIRC, isn't directly derived from the as actions of the Roman official, but more from those of the Catholic ecclesiastical official of the same name (sometimes more fully “censor librorum”) who reviews books intended for publication and provides (or withholds) the nihil obstat certifying it free of anything harmful to good faith and morals, which is generally a prerequisite to the episcopal imprimatur allowing it to be published, a function which is very much in line with the modern English understanding of censorship.