Censorship is important because of its potential influence on citizens' rights to free speech. It's also important because of the perceived need and practice by some to limit the availability of information for various reasons.
The U.S. Constitution guarantees U.S. citizens the right to free speech in the First Amendment. This means that the government cannot, according to the constitution, limit any person's expression no matter if that expression is offensive to some or most people or even completely false. While a celebrity could sue for slander and win in the court if someone defames the celebrity's name, for the most part, the right of free speech is not limited. At the same time, censorship has existed for a range of reasons at various points in American history. One might argue that censorship of information on military strategies helped the United States to win wars and that this would be a good reason in favor of censorship an example of censorship for the common good. It is much harder to argue in favor of the kind of censorship that went on during the McCarthy era in the 1950s, when anyone thought to be connected to Communism did not have the right of free expression. It might be even harder to argue in favor of censoring the publication of state secrets that have a significant, negative impact on the rights and freedoms of citizens. Censorship is a hotly debated topic because of the conflict between freedom and common good.