You can turn your community notifications on or off by clicking on the icon on a community's page.
Community members can use notifications to know when new things are shared with their communities. If notifications are On you'll get a notification by email, on your device, and by the Google toolbar when someone posts something new.
Notifications default on in communities where the membership is moderated - that is, private communities, or public communities where you need to ask to join. It's also on by default for any community you create.