A file that stores configuration setttings which you will find in the root folder of Joomla installation. All the parameters under the Site, System and Server tabs in the Global Configuration are stored as values in this file. This file is set up automatically by the software installation process and thus many of the parameters appearing in the Global Configuration screens are best left as their initial settings.

The word "core" in Joomla! pertains to the distributed files which are needed to create and administrate a Joomla CMS powered web site. These files can be downloaded from the Joomla website at http://www.joomla.org/download.html. The Joomla "core" also contains some basic functionality to get new Joomla installations working quickly and easily. Included are the user manager, article manager, weblink manager, category manager, contact manager, and menu manager. There is also a template manager with a few basic templates to power the front-end (website/user) view, a module manager with basic modules, plugin manager with basic plugins, and a few other "out of the box" extensions to extend the functionality of a basic Joomla installation. These core's extensions should not be confused with extensions which are available for downloading from the JED (Joomla! Extension Directory).

Reference: http://docs.joomla.org/Glossary