Joomla!® Core - this is a term, or phrase, that you are likely to hear or read quite often.
So, what is "Joomla Core" ?
Joomla Core is a term used to describe (or refer to) the folders and files that make up your installation of Joomla.
These are the folders and files that exist after a complete and fresh installation of Joomla.
While Joomla is extendable, like on your PC or laptop - you can add components, plugins, and modules to your Joomla CMS.
When you add extra components, plugins and / or modules - Joomla Core is what your website is or contains without these extra components, plugins or modules.
While it is possible to alter (edit / move / delete)Joomla Core files and/or folders - this is highly discouraged.
Changing Core Joomla folders / Files can cause major issues to the operation of your Joomla website.
Some features may stop working, others might not work properly.
Some, if not all developers of extensions will not provide support if their extension does not work after Joomla Core folders/files have been changed.
Also, changes to Joomla Core folders / Files will probably be over-written when there is a Joomla update.