>What exactly is the volume serial number?

It's an arbitrary hex identifier for a volume created on a given system.

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>Is different for each hard drive or CD Rom?

Created on a specific system, assigned by the system, yes. However, the user can specify a value during it's creation.

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>Is it Unique between computers?

No. Because it's user-assignable, it's not even guarenteed to be unique on a single syste, and, for example, when bulk-burning CDs, won't be unique among a given set of CDs.