super users, super users

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In Terminal, the password doesn't show when you're typing the password. When you've finished typing this, hold Enter key

Is User an administrator?

Are you actually trying to log in as root or are you trying to run sudo?

Just for quick background, there are different kinds of accounts on a unix sysem, with different abilities. Standard user accounts have access restricted to their own files, administrator accounts have access to system functions. There's also a root user that has complete access to everything; that's what's usually meant by superuser. Each user and administrator account has its own password, and if you only have the password for a standard user acocunt, you won't be able to access any of the system administrator or root level functions. Does that help?