In order to export a database using CUBRID Manager, you need to right click on the database name and go to Manage Database -> Unload Database.
Important! The database must be stopped in order to be able to run "Unload Database". If the database is running, then the option is disabled.
In the next screen, simply choose the location where you want the files to be exported to. There will be 3 files: demodb_indexes, demodb_schema and demodb_objects (assuming the database is named "demodb"). The first one holds the index definitions for each table, the second one contains all the table definitions, while the objects file contains all the data.