You will receive the New comment on your activity notification when someone comments on your activity or any activity where you have already commented or liked.
By email:

Click . You will be taken to the activity with all comments expanded and the comment box opened that is ready for your reply. The comment of this notification is highlighted.
Click . You will be taken to the activity with all comments expanded and the comment of this notification is highlighted.
Or directly on-site:

By clicking on this notification stream, you will be redirected to the full discussion.