When  you think you’ve turned off Facebook notifications in your settings but still get some, this is what you can do:

Unfollow a Facebook post from the new notification box.

1. Click the globe icon
2. Hover your mouse over the notification you want to stop seeing and click the X that appears
3. Click Turn off (or unfollow).

“Close friends” can generate a notification.

When you add one of your friends to your Close Friends list, you’ll automatically receive notifications about what that friend posts on Facebook. You can adjust the settings for these notifications:

1. From your news feed (Home button), click Friends in the left column. You might have to click More to see the Friends section.
2. Click Close Friends to view the list.
3. Click the Notifications dropdown in the top-right corner.
4. Choose whether you want to turn off these extra notifications.

Alternatively, you can keep notifications on for close friends, but remove people from the close friends list that you don’t want to receive notifications for.

Source: http://howto.cnet.com/8301-11310_39-57437395-285/easily-unfollow-a-facebook-post-from-the-new-notification-box/
Source: https://www.facebook.com/help/?faq=390022341057202&in_context