Think of a menu, not a kitchen. The API says what you can ask for and what you will get back. It does not require you to know how the other system stores its data.
A REST API is the most common style on the web: you ask for a resource over HTTP and get structured data, usually JSON. Good APIs have authentication, clear error messages, and limits so one client cannot knock the other system over.
Most of the cost in automation and custom software is not screens. It is these connections.