Whatsapp Web client is made for opening your whatsapp from browser. It gives users flexibility to login from multi platform. However your phone will need to stay connected to internet for web client to work. Your messages and other stuff will stay on your phone.
Logging in is very simple. Just go page and scan the QR code and you will logged into Whatsapp Web Client. You will be able to use it same as that of mobile version. You will need latest version of Whatsapp for web client to work.
Whatsapp is most widely used instant messaging service over internet with more than 600 million users across world. With this feature to rolled out there is most probable chance for Voice Call features to be coming to whatsapp soon.