An API extension is a security controlled set of functions and objects that are loaded on demand. These extensions are requested by the widget by listing the required and the optional extensions (if any) it wants loaded in its metadata.desktop file. This way, even prior to the widget being loaded, Plasma can know what it will want.
Required extensions are requested using the X-Plasma-RequiredExtensions key, and optional extensions with the X-Plasma-OptionalExtensions. For example: