Obi devices are standalone boxes which normally connect to your router and modem. You might have a cable or telephone line that comes into your house, then goes to a modem, then either goes directly to your PC or through a router which allows multiple PCs or devices to connect at the same time.
You would plug the Obi into the router. Then you would plug a telephone (wired or cordless) into the OBi.
You pick up the phone, the obi gives you a dial tone. You dial a number and the Obi connects with GoogleVoice to make the call.
You would not need a computer (except to set up your Obi and GoogleVoice to begin with). Your computer would not need to be powered on to make and receive calls. The Obi and Google are your phone company.
Google is primarily used within the US and may not work from other countries.
There are services that for a few dollars a month would allow you calls, but not free like Google. You would pay a small charge to make and receive calls. These services work well with Obis and other devices.
Callcentric has a free telephone number available but it is in New York City. Inbound calls are free but you would pay to make outbound calls, etc.
There are services like old Magicjack and Skype and so on which can use devices to make calls from computers and so on.
http://voip.planet-aloha.com/