Apple push notifications

Check out this article:

Use notifications on your iPhone, iPad, and iPod touch

Specifically, you might find these steps helpful:

Change alert styles

1. Go to Settings and tap Notifications.
2. Select an app under Notification Style. 
3. Under Alerts, choose the alert style that you want. If you turn on Allow Notifications, choose when you want the notifications delivered — immediately or in the scheduled notification summary.