Question: What additional privileges does the root user have over a standard user in Linux?

Answer: 
On Unix, users are represented by a number (User ID, or UID). Any user with UID 0 is privileged, normally there is only one called `root`.

Unix system permissions are more or less represented as permissions (the typical rwx) on files (devices, like disks, are also files for Unix). One of the differences is that root can override any read and write permission.

Another permission area is the manipulating of processes, something usually only the owner of the process (typically whoever started it, unless it is a SUID executable) is allowed to signal a process or attach to it for debugging. Again, root can override this.

Some operations (like powering off or rebooting) explicitly check for root.

Note too that modern security frameworks can be used to limit and grant privileges in a separate, fine-grained form. See [this thread](https://unix.stackexchange.com/questions/106595/myth-or-reality-selinux-can-confine-the-root-user) for some details on machines with `root` with no password, open to the whole 'net.
root is the system administrator, and they can do whatever they want to the system, which can lead to data corruption if the account is not used wisely. Since it appears you are new to Linux, I would recommend you not use root until you get more experience with Linux. To access an administrator/root command prompt from a standard users command prompt, type `su` (I believe most distros support this) and then hit enter.

*Beware when using root, as you can really mess up your computer.*