If you go to "Content", "Category Manager", you can unpublish categories by clicking on the green tick icon.
What's the point of doing so? The articles in that category are still published and still publicly available.
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your supposition that articles in that category are still publicly viewable isn't true.
Unpublishing a category, makes the articles in that category unavailable for viewing to site visitors/users.
Even unpublishing a parent category automatically makes the articles in its child categories unavailable for viewing.
With categories you filter through content. Say I have an article and I want to display all the content associated with the category of "Cats". This category needs to be published in order for the filtering to work.
This is primarily useful for blog posts, or if you have a shopping cart. The idea is to get all these similar things onto one relative article with as little effort as possible.
Hope this helps!