Yes as Olly said. Clay is used to remove the particles on the paint you can't see. It preps the surface ready for polishing so the pad stays clean for as long as possible. Also used to make the paint silky smooth.
If you want to remove the swirling then you need to get it polished. Either buy a Detailer or by buying a machine and having ago yourself.
You will only get rid of swirl marks by either having the car professionally detailed or by using paint renovator (like Autoglym Bodyshop 02B/03B) by hand (hard work) or with a dual action polishing machine like a Kestrel DAS6 or Meguiars 220.
To really learn about car detailing and looking after your paintwork I'd suggest a few hours browsing A world for detailers...