The configuration API provides a central place for modules to store configuration data. This can be simple static data like your site name, or configuration for more complex business objects like field definitions or image styles.
The configuration system is meant to replace contrib solutions like CTools Exportables, and enhance modules like Features.
In Drupal 8, contrib module developers can commit YAML files in a module/config folder defining the structure of their configuration settings.
For tasks related to conversion of all core system variables into the new configuration API, see #1775842: [meta] Convert all variables to state and/or config systems.