These two settings give you control of when authors and administrators receive notification that comments have been made, or that comments are held for moderation. Please note that the use of “me” refers to either a post author or the administrator (person whose email address is used for admin purposes).
Anyone posts a comment
Check this box so that every single comment posted will generate an email to the author of that post. Be warned that if your posts receive a large number of comments, post authors may find a very full email Inbox. The email you’ll receive looks like this:
If this option is unchecked you’ll only get an email for new comment moderation (if you account role has appropriate permission). Please read the next option description.
A comment is held for moderation
Check this box if you want WordPress to send notification that a comment is being held for moderation. The email notification is sent to the E-mail address listed in the Administration > Settings > General Screen. This is useful if your blog has multiple authors and each author is authorized to allow or decline comments. That way, you, the owner of the site, can review what comments are being allowed or denied. The email you’ll receive looks like this:
Please note, if this option is also unchecked you’ll not get any notification about new comments. Unless you’ve subscribed to certain post comments using wpDiscuz front-end options: