How does it work

i was curious what is actually happening when you plug mybook live first time to the router

Does it broadcast signal and register itsekf with WD servers?

Once thats done every time you access mobile app you are actually connecting to WD servers?

Does anyone know this inner working?

If you mean how the MBL does remote access, it’s by using  WebDAV. Check the link below for more info. 

http://en.wikipedia.org/wiki/WebDAV