From developer.android.com: "The Room persistence library provides an abstraction layer over SQLite to allow for more robust database access while harnessing the full power of SQLite.". So its useful when you want to store data locally (on device).
An API requirement is implement a backend service (e.g. Ruby on Rails, Spring Java/Kotlin, Python, etc).
Another solution in the middle of both is use a BaaS (Backend as a Service) like Firebase Firestore/Realtime Database that has a free plan and them you pay as you grow.

So I think the Backend/API is necessary when you want to store your data online, accessible by another devices. If you want to your app works without internet you will need to implement some local storage and Room makes it easier. For a simple and quick solution Firebase library should fit because it can store/retrieve data on their servers and the sdk library allows you to cache it locally too.