How to trigger push notification from device?

Hi,

I don't really get the concept of triggering a push notification directly from the app

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