Firebase is a Backend-as-a-Service (BaaS) app development platform that provides hosted backend services such as a realtime database, cloud storage, authentication, crash reporting, machine learning, remote configuration, and hosting for your static files.
Firebase supports Flutter. For more information, see:
- Getting started with Firebase and Flutter in the Firebase docs
- Firebase for Flutter codelab
- FlutterFire plugins
- Using Firestore as a backend to your Flutter app (video)
Also, the Flutter community has created docs that you might find useful: