In your WordPress admin at Settings>Discussion, if either of the two options are checked next to, “E-mail me whenever”, then an email will be sent out according to the option selected:
- Anyone posts a comment
- A comment is held for moderation
Otherwise there will be no notification emails sent.
If either or both of those settings are checked, then an email will be sent to the author according to which of the above are checked.
If in your WordPress admin at Settings>Discussion, either of the two options are checked next to, “Before a comment appears”,
- An administrator must always approve the comment
- Comment author must have a previously approved comment
then the website admin will also receive an email, unless the website admin is the same as the author – in which case one email will be dispatched to that one email address.
The email address for the website admin is specified in Settings>General as the “Email Address”.
The email address for the author is specified in their user profile. You can view the author of a post or page by viewing “All Posts” or “All Pages” and clicking the “Quick Edit” link under the post or page in question.