The term "censorship" comes from The Latin, censere "to give as one's opinion, to assess." The Roman censors were magistrates who took the census count and served as assessors and inspectors of morals and conduct.

In contrast to that straightforward definition from Roman times, contemporary usage offers no agreed-upon definition of the term or when to use it. Indeed, even whether the word itself applies to a given controversy in the arts is often vigorously contested.

Here are excerpts of definitions of "censorship" from U.S. organizations and publications with varying views. They are not intended as any composite mega-definition of the term, only as indications of the variety of approaches to this concept.

Censor: One who supervises conduct and morals: as a) an official who examines materials (as publications or films) for objectionable matter; b) an official (as in time of war) who reads communications (as letters) and deletes material considered harmful to the interests of his organization. Censorship: The institution, system or practice of censoring; the actions or practices of censors; esp : censorial control exercised repressively.
--Merriam Webster's Collegiate Dictionary

Censorship: The use of the state and other legal or official means to restrict speech.
--Culture Wars, Documents from the Recent Controversies in the Arts, edited by Richard Boltons

In general, censorship of books is a supervision of the press in order to prevent any abuse of it. In this sense, every lawful authority, whose duty it is to protect its subjects from the ravages of a pernicious press, has the right of exercising censorship of books.
--The Catholic Encyclopedia (a publication of the Catholic Church)

What Is Censorship? Censorship is the suppression of ideas and information that certain persons -- individuals, groups or government officials -- find objectionable or dangerous. It is no more complicated than someone saying, "Don't let anyone read this book, or buy that magazine, or view that film, because I object to it!" Censors try to use the power of the state to impose their view of what is truthful and appropriate, or offensive and objectionable, on everyone else. Censors pressure public institutions, like libraries, to suppress and remove from public access information they judge inappropriate or dangerous, so that no one else has the chance to read or view the material and make up their own minds about it. The censor wants to prejudge materials for everyone.

For the ALA, technically censorship means the "The Removal of material from open access by government authority." The ALA also distinguishes various levels of incidents in respect to materials in a library which may or may not lead to censorship: Inquiry, Expression of Concern, Complaint, Attack, and Censorship.
--The American Library Association

The word "censorship" means "prior restraint" of First Amendment rights by government.
--Morality in Media (Morality in Media is "a national, not-for-profit, interfaith organization established in 1962 to combat obscenity and uphold decency standards in the media.")

Censorship
1. The denial of freedom of speech or freedom of the press.
2. The review of books, movies, etc., to prohibit publication and distribution, usually for reasons of morality or state security.
--Oran's Dictionary of Law

Censorship: official restriction of any expression believed to threaten the political, social, or moral order.
--Encyclopedia.Com

Censorship - the prevention of publication, transmission, or exhibition of material considered undesirable for the general public to possess or be exposed to.
--Fast Times' Political Dictionary (Fast Times is "a nonpartisan publication on contemporary world affairs & media with no political, ideological, or religious affiliation of any kind.")

Censorship: the cyclical suppression, banning, expurgation, or editing by an individual, institution, group or government that enforce or influence its decision against members of the public -- of any written or pictorial materials which that individual, institution, group or government deems obscene and "utterly" without redeeming social value," as determined by "contemporary community standards."
--Chuck Stone, Professor of Journalism and Mass Communication, University of North Carolina

Censorship is a word of many meanings. In its broadest sense it refers to suppression of information, ideas, or artistic expression by anyone, whether government officials, church authorities, private pressure groups, or speakers, writers, and artists themselves. It may take place at any point in time, whether before an utterance occurs, prior to its widespread circulation, or by punishment of communicators after dissemination of their messages, so as to deter others from like expression. In its narrower, more legalistic sense, censorship means only the prevention by official government action of the circulation of messages already produced. Thus writers who "censor" themselves before putting words on paper, for fear of failing to sell their work, are not engaging in censorship in this narrower sense, nor are those who boycott sponsors of disliked television shows.
--Academic American Encyclopedia

Censorship: supervision and control of the information and ideas circulated within a society. In modern times, censorship refers to the examination of media including books, periodicals, plays, motion pictures, and television and radio programs for the purpose of altering or suppressing parts thought to be offensive. The offensive material may be considered immoral or obscene, heretical or blasphemous, seditious or treasonable, or injurious to the national security.
--Encarta Encyclopedia