What is a Push Notification? -Clickipedia

What a Push Notification is: Push notifications use push messaging technology within an application to send information to your phone, even when the app isn’t open or in use. A user may click on your notification to open, and be redirected to your app for follow-up.

What a Push Notification looks like: If a user enables push notifications for an app (such as a weather or sports application), the user will receive important messages or updates from the service. For example, a weather app, even when not in use, can send severe weather alerts to any push notification subscriber, or a sports app can send the latest score updates about a user’s favorite teams.

Why Push Notifications matter: Push notifications not only help your user and facilitate a relationship with your brand, but they help to keep your app top-of-mind—and most importantly, relevant.