denishua

When a reply is made to a comment the user has left on the blog, an e-mail shall be sent to the user to notify him of the reply. This will allow the users to follow up the comment and expand the conversation if desired. 
Detail information: http://theme10.com/comment-reply-notification/
中文介绍： http://fairyfish.net/2008/11/03/comment-reply-notification/

Comment Reply Notification

When a reply is made to a comment the user has left on the blog, an e-mail shall be sent to the user to notify him of the reply.

treeflips

Yin Zhongzhen

This simple plugin automatically sends a notification email to commenters when someone replies to their comment. This feature can be enabled automatically by the site admin, or through an opt-in/opt-out checkbox below comment section on frontend.
It’s best to use it with an email-sending plugin like WP Mail SMTP, and with SMTP or transactional email service like SendGrid or Mailgun. Sending from your server via PHPmailer can cause deliverability issues (email notfications caught in spam).
I loved the original plugin <a href="https://wordpress.org/plugins/comment-reply-notification/" rel="ugc">Comment Reply Notification</a> (by @denishua) for its simplicity but it was abandoned and stopped working years ago. So I forked and revived it to work with the latest PHP and WordPress. I also improved some wording, removed unnecessary author links in the email notifications, and also keep it more updated. Credits to Denis who first hacked it 5 years ago, and later Walter for fixing string escapes.
<h4>Features:</h4>
<ul>
<li>Feature modes – disabled, author/admin replies only, automatically, checkbox opt-in.</li>
<li>Edit email notification – subject and message.</li>
<li>[year] shortcode for dynamic year in email templates.</li>
<li>Developer-friendly hook for adding custom shortcodes.</li>
<li>Fixes issue with email notifications for moderated comments.</li>
<li>Can delete plugin options – after deactivation.</li>
</ul>

Comment Reply Email

Commenters can receive email notifications of replies to their comments.

Comment Reply Notification vs Comment Reply Email