The discussion settings area controls how your WordPress website handles comments. You may not want to allow comments on your site at all, but if you do wish to have comments then you should determine how you want to moderate those comments. To remove comments from your site, simply uncheck the first three boxes in the default article settings section.
Trackbacks and Pingbacks give bloggers an ability to communicate between websites. If your website’s main focus is blogging, you may want to read up on trackbacks and pingbacks at this site: http://www.wpbeginner.com/beginners-guide/what-why-and-how-tos-of-trackbacks-and-pingbacks-in-wordpress/. If your site does not have a blog then, you should disable them.
Attempt to notify any blogs linked to from the article – If you check this box, WordPress will send out a message to a site or article you have linked to in your post. Your mention of their site or article will show up in the comment section of their site, if that site allows pingbacks.
Due to a high level of trackback spam over the last few years, it is best to disable link notifications from other blogs by unchecking the box. You should also disable the attempt to notify option.
WordPress gives you some control over how strict you moderate comments. It is best to ask new users to fill out their name and email address. If you want more control, you can ask visitors to register in order to leave a comment. Alternatively, you can manually approve all comments to ensure that no spam or offensive comments go through. You can even blacklist comments that contain bad language if you wish.
If you uncheck the allow people to post comments on new articles option then any existing pages or posts (created before the check was removed) will still have a comment form attached to them. You will have to delete the page or post and then create it again, the new page or post will not have the form.
You can choose to enable or disable Avatars at the bottom of the discussion settings area. You can choose the default avatar for those who do not have a custom avatar of their own.