Paul W. answered 11/17/19
Dedicated to Achieving Student Success in History, Government, Culture
Keeping in mind that there are a wide variety of 'governments' around the globe and that these governments may use a number of different justifications for censoring the internet or cutting their citizens off from access to the internet, by far the most common justification is referred to as 'National Security.'
'National Security', however, means many different things depending on the government in question. Moreover, even for the government of a specific country, what qualifies as 'National Security' can change over time as circumstances change.
It might be useful to look at two distinct examples of the use of the term 'National Security' in relation to access to the internet.
The leaders of the People's Republic of China - an authoritarian, undemocratic, single-party state - are, above all else, determined to protect their hold on their power over the people they rule. These leaders equate their hold on power with the good of their nation, thus viewing anything at all that even potentially threatens their hold on power as a matter of 'National Security.' In other words, the 'security' (hold on power) of the leaders of the P.R.C. is the same in the minds of the leaders of the P.R.C., as the security of the nation.
It's understandable, therefore, that the leaders of the P.R.C. severely restrict the access of the Chinese people to the internet, claiming that their actions are motivated by concerns for 'National Security.' Of course, the reality is that access to the internet is restricted so that the people of the P.R.C. cannot either post or read about criticism of the leaders of the P.R.C. or use the internet to organize protests against government injustice and corruption.
The leaders of the United States - a liberal (if flawed), multi-party democracy - are, to one degree or another, accountable to the people who elect them (to a large degree they are held accountable by a free press). These leaders exercise the responsibility of protecting the lives and property of U.S. citizens. Therefore, when 'National Security' is invoked as a justification for interfering with the internet, it usually involved something that is perceived as an actual threat to the people of the United States, such as an impending terrorist attack.
Of course, even in the United States, interference in the internet is controversial, and rightly so. One of the chief rights guaranteed to citizens in the Constitution is that of free speech. Curtailing free speech by taking something off the internet has to be for a very serious, life endangering reason. As was demonstrated by the (over)reaction of the U.S. government to the 9/11 attack, 'National Security' can be invoked as a reason to trample on the rights of citizens guaranteed by the Constitution.
Again, the justifications of a government for censoring the internet or cutting off access to the internet varies a great deal according to the government in question and the time in question. Justifications can be sincere and wise or they can be abused simply to allow leaders to do what is in their interest and not in the interest of the people they rule.