Detailed Explanation
An API may describe the ways in which a particular task is performed. In procedural languages like C language the action is usually mediated by a function call. Hence the API usually includes a description of all the functions/routines it provides. For instance: the math.h include file for the C language contains the definition of the function prototypes of the mathematical functions available in the C language library for mathematical processing (usually called libm). This file describes how to use the functions included in the given library: the function prototype is a signature that describes the number and types of the parameters to be passed to the functions and the type of the return value. The behavior of the functions is usually described in more details in a human readable format in printed books or in electronic formats like the man pages: e.g. on Unix systems the command man 3 sqrt will present the signature of the function sqrt in the form:
That means that the function returns the square root of a positive floating point number (single or double precision) as another floating point number. Hence the API in this case can be interpreted as the collection of the include files used by the C language and its human readable description provided by the man pages.
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