When a library, DLL, Framework, or remote service is made available, with subroutines made available for other programs to use, the subroutines, their names, the parameters they take, and the types of data those subroutines return are called the application programming interface.
In other words, when a program makes a call into one of the subroutines to get work done, it can only do it through one of the public subroutines. There may be plenty more capability inside the library that provides the API, but only the routines exposed publicly can be called by external programs.