Local EAP is an authentication method that allows users and wireless clients to be authenticated locally on the controller. It is designed for use in remote offices that want to maintain connectivity to wireless clients when the backend system becomes disrupted or the external authentication server goes down. When you enable local EAP, the controller serves as the authentication server and the local user database, so it removes dependence on an external authentication server.
Reference: http://www.cisco.com/c/en/us/support/docs/wireless/4400-series-wireless-lan- controllers/100590-ldap-eapfast-config.html