The stems on saddle hackles are not perfectly round. If you tie a hackle stem right to the hookshank the stem of the feather will roll trying to find find a flat spot. When the stem rolls the entire feather to rolls.
The target fly is usually a flat winged fly but without the pillow the feather will usually roll on its side so the saddle won't lay flat and the fly loses all the attributes of flat saddles.

The pillow creates a bed/foundation for the feather to sit in so you can tie it flat and it will stay flat.

The pillow is easy to make. All it really is a few turns of dubbing wrapped around the hook where you want the feather to lie. Usually we use the webbier feather barbs at the base of the feather instead of fur for the dubbing, seeing as we peel it off the feather as waste anyway.

The steps to these flies seem unneccesary but are important to the mechanics of how the flies swim once they are in the water.

http://www.stripermoon.com/flies/ecg.html