The Free On-line Dictionary of Computing (30 December 2018):

Application Program Interface
API
Application Programming Interface
Applications Programming Interface

    (API, or "application programming interface")
   The interface (calling conventions) by which an application
   program accesses operating system and other services.  An
   API is defined at source code level and provides a level of
   abstraction between the application and the kernel (or
   other privileged utilities) to ensure the portability of the
   code.

   An API can also provide an interface between a high level
   language and lower level utilities and services which were
   written without consideration for the calling conventions
   supported by compiled languages.  In this case, the API's main
   task may be the translation of parameter lists from one format
   to another and the interpretation of call-by-value and
   call-by-reference arguments in one or both directions.

   (1995-02-15)