If you follow a task, you will be notified about activities happening on the task e.g. when someone adds a comment or when someone attaches a file. The notifications will be through email as well as through the notification center. If you are an assignee or a project manager, then you are automatically notified and there is no need to explicitly follow the task.
To unfollow a task, simply click on the Unfollow link on the task screen on in the footer of the email notification.