To access the client, head on over to https://web.whatsapp.com/ and scan the QR code (follow the instructions for your specific handset).
With my Sony Xperia C it's easy.
Then you've got a WhatsApp chat client from your desktop! The only catch I can see so far is that it will need to do a fairly regular stream update with your device but I suppose that's the same for any other of the integrated apps like Hangouts, Facebook, etc.
And you can coordinate your devices from the WhatsApp Web menu
doesn't support iPhone yet
chats work well but you need to have an active Internet connection on your phone for it to work, if the connection on your mobile is down, then the web client won't work - this is something that Hangouts has covered, so WhatsApp has some flaws.
WhatsApp Web is an extension of WhatsApp on your phone; it connects to your phone to sync messages - kind of a strange solution so not BETTER than alternatives like Google Hangouts. I still think Hangouts is the shizz.