Jetpack plugin provides you feature to allow your commenters on follow up comments. There are also many other free plugins available in WordPress Plugins Repository that allows you to add comment subscription system in WordPress. This tutorial is a bit different, it explains you how you can allows your commenters to get notified only when someone replies to their comment in your WordPress site.
Install and activate Send Email only on Reply to My Comment. After activation you can easily manage subscriptions, stats and other options your admin area Dashboard -> Settings -> One Email.
Your visitors now can easily subscribe to email notification on comment reply by checking the small tick box this plugin automatically adds in WordPress comment form.