With Backend Services you can make a one-time import of the data in the catalog tables in a content type in the cloud or connect your database tables to the cloud and use them with a REST API in your app.
One-time import of data
Create a intermediary layer, for example, with an ORM tool that can read items from the database and convert these items into Backend Services objects and save them in your backend project. For example, from your SQL entities, construct objects following this Object Model
and save the items in Backend Services.
Connect your SQL database to the cloud
I'd suggest that you take a look into this Getting Started article
Let me know if the above answers your question and if you have further questions.