Following a Buzz means you have opted in to receive notifications/alerts about that Buzz, for instance when someone posts a comment, or the Buzz is edited.
When you create a new Buzz yourself, you as the owner automatically follow it. When you create a Buzz using the New Conversation template, all participants are automatically set to Follow the Buzz so they will receive your messages - they can still manually opt out on the Buzz itself, or opt out directly from the notification emails.
Simply click toggle the ‘Follow?’ button in the Buzz header. If you are following a Buzz, the same button switches to ‘Following’ - click it again to unfollow stop receiving notifications for that Buzz.
Click the Buzz options button (the 3 dots at top right), and check or uncheck the ‘Following’ toggle on the Options screen.