How to trigger push notification from device?

Hi,

I don't really get the concept of triggering a push notification directly from the app Image may be NSFW.
Clik here to view.

My goal is to trigger push notifications directly from the devices that run my app.
For example, if a user creates a new "event", all other users should get a notification.

My questions are:
* What is the best way to trigger push notification directly from the app?
* Is it possible to use the push api directly from the app?
* What is the concept of using another backend server that communicates with the push api?

I'm using Firebase as the data backend.

Thanks a lot,
Michael