Simple and self-contained apps like calculators, magnifier, invoicing or drawing apps don't need their own backend service, an API or a server farm to serve content for thousands or even millions of users.
Generally, apps that ask their users for sign up or games where users want to interact/play with other users need a backend service. Another use case would be to serve content to all your users which is authored and edited in a third party content management system.
There are some differences between backend services. Not everyone needs to build its own custom backend service. Pre-engineered backends are available like Apple CloudKit or Firebase.
Only if you have non-trivial functionality you need to build your own custom backend for your mobile app.
Good examples for apps that need a custom backend service are messaging apps, live streaming apps or health/fitness apps.