Manual:$wgExtensionFunctions

Details
This variable is an array that stores functions to be called after most of MediaWiki initialization is complete. Note however that at this point the RequestContext is not yet fully set up, so attempting to use it (or equivalent globals such as $wgUser or $wgTitle) is liable to fail in odd ways. If you need to use the RequestContext, consider the BeforeInitialize and ApiBeforeMain hooks instead.

This variable should be used for final step of initialization of extension setup code that needs to perform advanced things, like using global functions and instantiating autoloaded classes. Typically each extension has one setup function associated with it. The array element concerned is typically defined in the extension file itself, with a statement of the form compatible with call_user_func PHP function:

Each setup function is then called from /includes/Setup.php.

For example, if your extension needs to access database during its initialization:

Semantic MediaWiki
It used to be recommended for the optional configuration of Semantic MediaWiki to be placed in a $wgExtensionFunctions call, up to 1.8. Don't do this in Semantic MediaWiki 1.9 or higher (it now uses composer), the configuration will not work.