A backend in curl is a build-time selectable alternative implementation.
When you build curl, you can select alternative implementations for several different things. Different providers of the same feature set. You select which backend or backends (plural) to use when you build curl.
Backends are selectable and deselectable
Often platform dependent
Can differ in features
Can differ in 3rd party licenses
Can differ in maturity
The internal APIs are never exposed externally
In the libcurl source code, there are internal APIs for providing functionality. In these different areas there are multiple different providers:
HTTP/1 and HTTP/2
HTTP content encoding
Applications (in the upper yellow cloud) access libcurl through the public API. The API is fixed and stable.
Internally, the "core" of libcurl uses internal APIs to perform the different duties it needs to do. Each of these internal APIs are powered by alternative implementations, in many times powered by different third party libraries.
The image above shows the different third party libraries powering different internal APIs. The purple boxes are "one or more" and the dark gray ones are "one of these".