The ParserFunctions extension enhances the wikitext parser with helpful functions, mostly related to logic and string-handling. Since MediaWiki 1.15, ParserFunctions has incorporated most (but not all) of the functions from the StringFunctions extension, which may be enabled or disabled (see install instructions hereafter).
This extension is being used on one or more Wikimedia projects. This probably means that the extension is stable and works well enough to be used by such high-traffic websites. Look for this extension's name in Wikimedia's CommonSettings.php and InitialiseSettings.php configuration files to see where it's installed. A full list of the extensions installed on a particular wiki can be seen on the wiki's Special:Version page.