Hello!
When the checkbox you see is checked, people will be allowed to write comments and have their comments published on a specific post. You can change the restrictions to how someone comments under Settings > Discussion.
When it says that it could be overridden by individual articles, that means that even if the site would generally allow comments on all posts, there are some specific posts that may be excluded from comments. In the Add Post page, where you write the post itself, there is a “Discussion” box with another checkbox to allow comments. This should override the settings specified in the general menu.
So, if in Settings > Discussion you have “Allow people to post comments on new articles” checked, then users who come to your site should be able to write comments on your posts. If, in a specific Post page, you uncheck the “Allow Comments” box, all other posts will be unaffected, but that specific post will not allow comments from users. The reverse is also true.
Hope that helps!
