What is an API? What is it an abbreviation for?
Application Program(mable) Interface. You see these two versions out there. And yes, it is software and patentable.
Maybe this?
“In computer programming, an application programming interface (API) specifies how some software components should interact with each other.
In addition to accessing databases or computer hardware, such as hard disk drives or video cards, an API can be used to ease the work of programming graphical user interface components. In practice, many times an API comes in the form of a library that includes specifications for routines, data structures, object classes, and variables. In some other cases, notably for SOAP and REST services, an API comes as just a specification of remote calls exposed to the API consumers.[1]
An API specification can take many forms, including an International Standard such as POSIX, vendor documentation such as the Microsoft Windows API, the libraries of a programming language, e.g., Standard Template Library in C++ or Java API. Web APIs are also a vital component of today’s web fabric. An API differs from an application binary interface (ABI) in that an API is source code based while an ABI is a binary interface. For instance POSIX is an API, while the Linux Standard Base is an ABI.[2]”
Source: Wikipedia
To put it simply, an API is a set of instructions a software company will put out for a piece of software, that delineates how a 3rd-party programmer can write applications that then interface with the original piece of software.