"Min" is the front end application index.php that handles requests to http://example.com/min/ and responds with compressed/combined content.
When the documentation refers to "Minify" it usually means this application, but sometimes refers to the ComponentClasses.
User-configurable files:
/config.php: general configuration/groupsConfig.php: configuration of pre-defined groups of files
Other files of interest:
/.htaccess: rewrites URLs for the front controller/index.php: front controller/lib/Minify/Controller/MinApp.php: determines which files are combined based on$_GET, sets some default options