Why, if I am the administrator of the machine, I do not know the password of the database?
Because on SME Server the root password is a random 72 charachter string for security reasons, by a clever mechanism you do not need to type, remember nor know it, because when you login to the SME Server shell as root and issue the mysql command it is automatically filled in.
Furthermore you should only use the root account for administration purposes and
never configure an application to use it, create a separate user with the minimal required privileges for the application and configure the appplication to use that user, please read the MySQL FAQ in the wiki as a lot of MySQL related stuff on SME Server is there, furthermore the MySQL manual itself is worth reading I guess.