They mean you can call by voip and the messages are sent over the phones internet.
I get it. But it doesn't make any sense to require that I have a carrier set up. I use wi-fi only on my tablet and can Skype using it just fine.
Oh you mean that. The thing is that they identify users by their phone number. When you add a new user in your address book then whatsapp automatically checks if he has whatsapp installed. If so you can chat with him and he shows up in your list. So its part of the usefulness that it sets on phone numbers. Im not sure if they could raise their market share by allowing users that dont have a phone number.