Sometimes you need to show a person on the other end of a phoneline something on your screen to bring your point across. Very often you don't know the person very well and - more importantly - they don't know you very well.
So why would they give you their Skype-Id, fire up Teamviewer, install a plugin for hangouts or other services just to do you a favor?
With connect.one you can simply give them a url like connect.one/delodi to show them what you have to show. Without any need for installation on their part, across any firewall and onto any browser.