You can read the set up manual here : click here
The "wireless" refers to connectivity with other PC's.
While the Olivetti web site doesn't seem to specify the power supply, I doubt it will be battery operated, and will more than likley need to be plugged into the Mains.
On first set up the Printer has to be connected to a PC by cable ( not supplied ! ), and can then be configured to be acessible on your home wireless network ( if you have one ).
So, once set up, if you have another PC in anothe rpart of the house on your wireless network, it should be possible for that PC to print to the new wireless printer.