Project page: Push Notifications on Drupal.org.
Push Notifications Overview
The Push Notifications module provides the feature set to send out push notifications to iOS (iPhone/iPad) and Android devices using Apple's Push Notification Service (APNS) as well as Google's Android Cloud to Device Messaging framework (C2DM) and/or Google's Cloud Messaging for Android (GCM). This module does not rely on any external services and allows site owners to send out push notifications to any mobile device for free.
Push Notification Settings
Navigate to /admin/config/services/push_notifications/configure to configure the push notification settings for APNS, GCM or C2DM.
Navigate to admin/config/services/push_notifications/message. On this page, you can compose a push notification to send out to all registered recipients. Enter your message, select the recipient groups (iOS, Android or both) and click on "Send Push Message".