Is "Private" private

When I set the Visibility of a post to “Private” does this mean that it cannot be seen on the web without my providing the link to someone?

I am seeing these posts when I simply go to the normal blog url and they all seem to show up in the Categories’ Section. They don’t show as counting in the parentheses (the number of posts in the category) but when you click on the category the posts show up with simply a “private:” and then the name of the post.

Shouldn’t these not be showing up??

Thanks.