ACLU definition
Censorship, the suppression of words, images, or ideas that are "offensive," happens whenever some people succeed in imposing their personal political or moral values on others. Censorship can be carried out by the government as well as private pressure groups. Censorship by the government is unconstitutional.
In contrast, when private individuals or groups organize boycotts against stores that sell magazines of which they disapprove, their actions are protected by the First Amendment, although they can become dangerous in the extreme. Private pressure groups, not the government, promulgated and enforced the infamous Hollywood blacklists during the McCarthy period.
Wikiepedia definition
Censorship is the suppression of speech, public communication, or other information. This may be done on the basis that such material is considered objectionable, harmful, sensitive, or "inconvenient". Censorship can be conducted by governments, private institutions and other controlling bodies.
Merriam Webster definition
transitive verb
: to examine in order to suppress (see
suppress sense 2) or delete anything considered objectionable
censor the news
also
: to suppress or delete as objectionable
censor out indecent passages
The U.S. Constitutional First Amendment Rights deal with protection from the government.
Censorship is a broader concept than just government suppression of ideas. Government censorship is a subset of censoring.