Can anyone explain this whole Facebook share stuff?

[GreyVampire]

The guy above has answered pretty much everything, but you asked if any company can do that. Well, no. Not really, anyway. There are two types of 'company' a Private Limited Company (LTD) and a Public Limited Company (PLC). A Private Limited Company is one that is registered as private, and will therefore have private investors and shares will not be sold to the public. A Public Limited Company is where shares are available for the public to buy at will.

In order for a company to change what type it is, it will need to re-register. This is how it works in the UK at least... not sure about other countries.