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The WordPress API stands for the WordPress Application Programming Interface. It can be separated into multiple API sections / topics. Each covers the functions involved in and use of a given set of functionality. Together they form what might be called the WordPress API, which is the plugin/theme/add-on interface created by the entire WordPress project.
If you've read through all of these you should have a good sense of how to extend WordPress through Plugins.
See also WordPress.org API.