When you first install MySQL you need to set a password for root to be sure nobody is going to access your Databases.
If your MySQL is a fresh installation you will need this command
mysqladmin -u root password newpassword
This is used when there is no previous password, if what you need is to change a password already set, you will need this other command.
mysqladmin -u root -p oldpassword newpassword
And finally if you want to change some other’s password (not root) use this command
mysqladmin -u someuser -p oldpassword newpass