No, that has nothing to do with Vonage. As far as a PBX goes (which is what you're referring to - having extensions, etc), Vonage is just another "dialtone provider".
I don't believe that Vonage offers business PBX hosting, but I do know that some companies do (most of them use Asterisk for this). In that case, you use telephones that are all attached to the internet, and the remote server takes care of the extensions, voicemail, etc. Don't expect it to be cheap.
If you're familiar with linux and aren't afraid to "get your hands dirty", check out the Asterisk phone system (Google it). It basically takes a computer and turns it into a phone system, and you can attach VOIP phones, analog adapters, or normal phones to it (with special hardware). Said hardware is also not that cheap, but it would be in the price range of many small businesses.