yes...
The wireless part just refers to the way the internet is transfered from the phone line to the computer, at the moment you will have a wire connecting your computer to the internet that comes in via your phone line. with wireless you have a wireless router that sends the internet to your lap top without using wires.
if you havn't already got one all you need is a wireless router (about 50quid max from somewhere like pc world) and then you can have both your desktop and your laptop connected at the some time to the interent.