First of all, you can spin raw fleece just how it is, unwashed, but most people want it washed first so...
The main thing you want to accomplish in washing it is to remove the lanolin (grease) which is what makes it smelly and sticky. The straw, hay and burrs will actually fall out of clean, dry wool as you draft and spin the yarn. Well most of it anyway. There may be tiny bits of hay left in the yarn, but I think it makes for a more charming, homespun looking yarn.
Mostly, you want to get the grease out. Here's how