What does unregister really do? Today I lost my iPhone and because of that I proceeded to unregister it from Apple as http://support.apple.com/kb/ht2526 indirectly suggests.

What does it really mean to unregister a product?
It removes it as being registered to your name in Apple's system. When you call Apple support from the iPhone, a screen pops up saying your name, the serial number of the phone, and information related to the phones previous issues. When you unregister it, that information goes away and it appears as a device that has yet to be registered. (Unless it is flagged as stolen).