Every topic, forum, blog and club has a Follow button. Following one means new activity in it turns up in your notifications, and — if you have asked for them — in your email.
You follow anything you post in automatically. That is why a thread you replied to once keeps telling you about itself, and it is also why Unfollow exists: it stops the notifications and leaves everything you wrote exactly where it is.
Your notification settings live under your name, in Settings → Notifications, where you can choose what reaches you on the site and what reaches you by email separately. They are separate on purpose: plenty of people want the bell and not the inbox.