Jenny, it goes under an English saddle and the purpose is so that only the borders are visible - a minimalist. In this case, using 100% wool just gives it a nice appearance and the thick border helps keep it from getting sucked up under the saddle.
Actually, while iridehorses was right about the half-pad's appearance and one use of it, that's not all it's used for.
Yes, half-pads are used at shows under a saddle so that the saddle will stay clean and you will look as polished as possible.
BUT the half-pad has other uses too. They are used on all the horses at my lesson barn to make sure that the saddles fit because people can bring their own saddles and there are many different lesson saddles. Half-pads also wick away moisture and keep the horse's back cool. They also help the circulation of the back. I like using half-pads, but there are many different opinions on them.
A simple half pad (no shims) just adds some thickness under a saddle and increases air flow. It does not cushion much and can make the saddle fit narrower (smaller), depending on how thick and dense the sheepskin is.
A half pad should NOT be used with a saddle that barely fits or is too narrow. It's like putting thick socks on with dress shoes. It's okay for a bit, but after a while... OUCH!
They look pretty, provide a tad bit of cushion (for a LIGHT weight rider), and can help a too-wide saddle fit a bit better.
For most riders and most horses, they are just a fashion statement, especially when you use a baby pad underneath like many people do. The point of the good sheepskin is for it to be against the horse's skin/hair. Otherwise, you're not getting the full benefit.
There is a girl that rides my TWH w/ an english saddle. The saddle fits fine but she uses one of those thin square english pads and it slips (the pad) really bad. So is a half pad what I should get her?