I'm not sure I understand the question. A push notification is simply a notification that you receive from an app when you're not using it. What triggers the notification could be web-based (e.g. a new email arrives on the server and the Mail app detects it and pushes a notification to you that you have a new Email) or local (e.g. a reminder comes due and the Reminders app pushes a notification to you that it's due). Does that help?