Security and privacy
Can you give more information, what is the exact text of the message you are seeing. What operating system, what type of moodle install (xampp?), when do you get the message. Have you created the database in mysql, i.e. if your config.php is expecting a database called moodle does that exist in your mysql instance?
Do not delete this user! The root user is the superuser in most linux systems. Please answer Marcus's questions for more help.
Learn about user groups in linux. You can change the owner of a file folder, but what is more important is that you belong to a group that has permissions to read, write, excecute a folder and contents.
Tell us more , good luck
If this user is showing up in Joomla and not Moodle you are probably talking to the wrong people as this site specialises in Moodle rather than Joomla. The root@localhost account can be a default account in Mysql, so if you type
it will return an error message saying access denied.
Access denied for user 'root'@'localhost
Now on shared hosting you generally don't get the root account to the database, otherwise you could mess with databases belonging to other users. Also on shared hosting (i.e. someone else is your web master), you are generally at the mercy of the super user because even if they don't have access to your database they will have control over the disk space that contains it and could do bad things. You need to trust them.
Of course that may not relate to your problem, it could be something to do with Joomla that is outside my experience.
Marcus is right. This is probably a Joomula issue related to Linux.
If root is not on your Moodle site, then you should be OK. You want to be sure in Moodle that any time a password or profie is changed for admin, you get an email.
I think the issue is that the Joomla interface can pass along authenticated users to Moodle.
If you don't trust your web master, you have the wrong person.