The computer's "specific ID" is calculated from the hardware characteristics.
I don't know if this applies specifically to Microsoft Office (I assume it does). From Microsoft's Product Activation FAQ:
How does Microsoft identify the computer's hardware?
Microsoft Product Activation detects the hardware configuration on which the product is being installed and creates hash values for that configuration. A hash is a value mathematically derived from another value - in this case hardware configuration values. Product Activation does not scan the customer's hard drive, detect any personal information, or determine the make, model or manufacturer of the PC or its components. Microsoft uses hash values out of respect for users' privacy. A hash value cannot be backwards calculated to determine the original value. In addition, Microsoft only uses a portion of the original hash values. Together, these hash values become the complete hardware hash that is included in the installation ID.