You’re the only user who can create posts and moderate comments on your WordPress installation.
You have both ‘Email me when anyone posts a comment’ and ‘Email me when a comment is held for moderation’ options checked.
You get an email about a comment awaiting moderation and you approve it.
The problem is that right after that you get a second email letting you know that a new comment has been posted, which of course you already know about.
Instead of disabling email notifications for new comments alltogether, you can use this plugin and not receive the redundant emails mentioned above.