From David Bolton,
Your Guide to C / C++ / C#.
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Definition: All Operating Systems provide a way for applications to use their system resources by using an Application Programming Interface or API. This is usually defined by an extensive list of functions and classes and variables

It's not just Operating Systems that provide APIs. Every programming library (and there are thousands available, both commercial or free) has an API. It's the job of a programmer to read and understand APIs so that he/she can make the best use of them.

Glossary:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Examples: DirectX is a collection of games programming APIs.